Do Jehovah’s witnesses believe that they have the only right religion?

That's something you would have come to the conclusion for yourself. Compare what Jesus Christ said his disciple would be like, the fruitage they produce and look at other religions and see what fruitage they produce. Do they sanctify God's name Jehovah as Jesus Christ said? Psalms 83:18, Luke 11:2 by using God's name when they pray to him in Jesus Christ's name? Are they maintaining Christian neutrality by being no part of the world by keeping free of their politics, not engaging in their wars, and not marching and protesting against the authorities? Are they preaching the Good News of God's Kingdom as the only solution to mankind's problems, do they believe that the Bible in it's entirety is the inspired word of God, do they have love amongst themselves no matter where in the world they live, do they show love for God and neighbor, do they live by God's word to the best of their ability? These are all important questions when searching for God. Jesus Christ said broad and spacious is the road leading to destruction and many are on it whereas narrow and cramped is the road leading to life and FEW are finding it.

We know that there are two road. One lead to life and  one leads to destroy. Matthew 7:“Go in through the narrow gate, because broad is the gate and spacious is the road leading off into destruction, and many are going in through it; 14 whereas narrow is the gate and cramped the road leading off into life, and few are finding it. 

The Bible tells us how to identify. 

We should worship only Jehovah. Psalm 83:18 says: “You, whose name is Jehovah, you alone are the Most High over all the earth.” Jesus wanted people to know exactly who the true God is, and he taught people God’s name. (Read John 17:6.)

We need to have genuine love for people. Jesus taught his disciples to love one another. (Read John 13:35.) It doesn’t matter where we’re from, what our culture is, or whether we are rich or poor. Our love for one another should unite us as brothers and sisters. (Colossians 3:14)

We need to obey Jesus because he is the way to God. The Bible says: “There is no salvation in anyone else, for there is no other name under heaven that has been given among men by which we must get saved.” (Acts 4:12) In Chapter 5 of this book, we learned that Jehovah sent Jesus to give his life as a ransom for obedient humans. (Matthew 20:28) Jehovah has chosen Jesus to rule as King over the earth. That is why the Bible tells us that we must obey Jesus if we want to live forever.​—Read John 3:36.

We should not get involved in politics. Jesus didn’t participate in politics. When he was on trial, he told the Roman ruler Pilate: “My Kingdom is no part of this world.” (Read John 18:36.) Like Jesus, we are loyal to God’s heavenly Kingdom, and for this reason, no matter where we live, we do not get involved in politics. However, the Bible commands us to obey “the superior authorities,” that is, the governments. (Romans 13:1)

We should not get involved in politics. Jesus didn’t participate in politics. When he was on trial, he told the Roman ruler Pilate: “My Kingdom is no part of this world.” (Read John 18:36.) Like Jesus, we are loyal to God’s heavenly Kingdom, and for this reason, no matter where we live, we do not get involved in politics. However, the Bible commands us to obey “the superior authorities,” that is, the governments. (Romans 13:1)

We believe that God’s Kingdom is the only solution for the world’s problems. Jesus said that the “good news of the Kingdom” would be preached all over the world. (Read Matthew 24:14.) No human government can do what God’s Kingdom will do for us. (Psalm 146:3) Jesus taught us to pray for God’s Kingdom when he said: “Let your Kingdom come. Let your will take place, as in heaven, also on earth.” (Matthew 6:10) The Bible tells us that God’s Kingdom will destroy all human governments and that “it alone will stand forever.”​—Daniel 2:44.

After studying these points, ask yourself: ‘Who base their teachings on the Bible? Who tell others about God’s name? Who show genuine love toward one another and believe that God sent Jesus to save us? Who do not get involved in politics? Who preach that only God’s Kingdom can solve our problems?’ It is only Jehovah’s Witnesses.​—Isaiah 43:10-12.

Jehovah witnesses think Jehovah is a name, they don't understand the use or purpose of a proper name, Jehovah is only a translated word for Yahweh made by a different generation because of their understanding of what they original word meant, it's only a title just as there are many other titles used for Yahweh, Yahweh means Lord, Lord means master over ALL, not lord, master over men, they also believe every single word in their version of their bible IS inspired by God not realizing the translators added that word " is " in the sentence, the original author didn't use that word but said " all scripture INSPIRED of God is profitable for doctrine " the translators wanted them to believe everything written was inspired by God, even Jesus knew this and referred to it as " their law ", the scriptures are what Paul was referring to when he wrote to Timothy and said, study to show thyself approved, rightly dividing the word of truth, divide means to separate, separate from what? obviously what God inspired and what man inspired, it's no different than going into another country and finding the name Jesus pronounced or spelled differently from English, the meaning is the same except to people that cling to traditional languages, they would probably freak out if they understood this, the meaning behind the word is where the POWER lies however it doesn't matter what they think His name is, for there is only ONE name under heaven that men can be saved and that name is JESUS in English, in a different language it might be spelled differently or pronounced differently but it's the same LORD that's LORD over ALL. IF they are following Jesus and His commandments they have the right religion just as any other denomination is, there is only ONE GOD and ONE LORD regardless of how the words are spelled or pronounce, the evidence of this is in the power of the word being used WITH the meaning of the word being known, not understanding the meaning of the word being used makes the word pointless to use, saying God to anyway has the same effect on everyone hearing it, they think of this powerful entity up in the sky that can do anything He desires, saying the name JESUS means nothing without explaining WHO He is, it's the explanation that is the meaning behind the word being spoken, without the meaning the word can only be assumed to mean something, the something can be confusion if there are more words with a likeness that mean the same thing, such as Jehovah, LORD God, the Almighty God, Immanuel, Savior, Prince of Peace, some would argue His name should be called Immanuel because that is another word used for Him by the author saying

Isa 7:14Therefore the Lord himself shall give you a sign; Behold, a virgin shall conceive, and bear a son, and shall call his name Immanuel. " He shall be called Immanuel " the meaning of this word is " God is with us or God is amongst us ", the signs concerning Jesus were all there, He was NOT named Immanuel " the meaning behind the word " He was named Jesus which is the English version but the same name spoken in a different language and written in a different form BECAUSE of the POWER in that name, the POWER to save but has to be explained, saved from WHAT? WHY? HOW? only a person with a conscience concerning SIN, LIFE and DEATH would even be interested in what your saying, JESUS deals with them ALL and BACKS UP everything He said in POWER or WITH POWER revealed by GOD from Heaven, the power to forgive sin's, the power to heal the sick, the power to raise the dead, the power behind the way to live, no other person born in all of history has this same power over life and death that has died and come back from the death and revealed Himself to others and still has the power to reveal Himself to others that never seen Him, saying the DAN GOD or the STEVEN GOD means nothing but confusion to the reader especially if the reader knows someone else named Dan or Steven, saying the Lord God or Yahweh God means nothing to the reader without understanding the meaning behind the word Lord and God, the significance of last names are important because of the number of people that have first names that are alike which is why Jesus was referred to as Jesus of Nazareth, Mary of Magdalene, the likely hood of others having the same name in other regions is why they used the town or city to identify who was being spoken or written about, Joseph " of " we adopted last names for this reason that has to do with population and so many having the same first name but still if others none by their names have others none by the same name, your going to be asked, WHO are you talking about? then your going to give a explanation which describes the name, the description is what matters, the description gives meaning to the name or a understanding of the word, the power behind the word is not the word it's self but the meaning of the word along with the understanding of the word being used, without the understanding your only going to get, " what do you mean " or " do you know what I mean " from the user and the listener, just reading the bible without a understanding of the words being used creates confusion because words are translated in a language of understanding of the language being used and because of this it would be wise to know the meaning behind the word being used from the original authors mind and not our own because we have this fault of assuming meanings based on traditions and customs of our own times and not theirs, nevertheless, Jehovah is only another word that means LORD, LORD meaning master over ALL, that would be Jesus  since ALL authority concerning mankind was given to Him by what many would call HIMSELF that can identify the Lord God as being HIM when in reality it was HIM that gave Himself that power because it was HIM in Spirit FORM that said to them concerning the one HE would APPEAR in WHEN He came, Moses didn't give them a name when they asked who sent you, Moses only told them He was going to appear to them, this is the true origins of the promise of the Messiah ( another title ) to appear or to come, held onto by oral tradition but lost in translation, I AM I AM has two meanings, one is present tense, the other is future tense, I AM or TO BE means I exist in the present tense, I AM or TO BE means to become or to appear in the future tense, just tell them I AM TO APPEAR or in better English, tell them I AM COMING, HE CAME already and they rejected Him although not ALL yet to those that did receive Him He gave the right to be called the children of God, if you don't believe in Him you have no right to be claiming your a child a God although many do but the evidence of this will be revealed on that DAY, the day of judgement, when JESUS judges the world, not by our own commandments but HIS, the same one's He gave Moses before He appeared and the same one which He revealed in love thy neighbor as thyself which is the meaning or the purpose the law was given of which will be the basis on which He uses to make His judgement concerning man, not on anyone's understanding of all these words used to describe Him but on their obedience to what He said of which no one will have an excuse since He has written His law on men's hearts, saved or unsaved. 

ALL religions try to assert that their religion is the correct one.  And it is STILL an epic fail.  Without proof and evidence to support it, all you have is an assertion.  An assumed conclusion.  Nothing more.

I think everyone who has a religion thinks they have the right religion until they start questioning doctrines, traditions and/or beliefs attached to that religion.

 Consider tithing. Jesus said we should give from our hearts, that may be more than 10% or less. I don’t remember seeing or hearing of Jesus’s disciples passing any plates, that may have been something that was added to a religions service. I hear it may be passed several times during a service!  And what about a job?  Jesus was a carpenter. He did not receive payment as a preacher or teacher. Some pastors get paid for their services. You might question is your religion following the example of Christ!

They top the list of "Most Dangerous Cults." 

The most ignored warnings are those of God.

Followers of Christ OBEY His Word to make room for the Trinity. After this, they are led by the Holy Spirit. One of the names God calls His Holy Spirit is the “Spirit of Truth” -- “Sacred Truth” the kind that exposes the Lie and crushes worldly wisdom, and helps us find the way home. Can you see why the Truth matters? I hope so. [John 14:17]; [John 14:23].

A false religious system claims as its authority some special revelation or teaching APART from the Bible. Many Christians are caught in this web because they believe everything they hear and don't read the bible themselves. Some lie to themselves; they’ve abandoned the old ways “the true value of humanity,” and developed a new taste for many strange things. In this case, 'inner death' while still alive. Could anything be worse?

So, let me take them all back to where the disobedient angels turned into demons [Revelation 12:3-4,9]; [2 Peter 2:4].

Now, the “Right Time” is the time you decide to make it right. Go back and read my second sentence and return before it’s too late.

The Bible says: “By their fruits you will recognize them. Never do people gather grapes from thorns or figs from thistles, do they?” (Matthew 7:16) Just as you can distinguish a grapevine from a thorn bush by what it produces, you can distinguish true religion from false by its fruits, or by these identifying features.

They certainly like to converge on residential areas at night in groups of 20 to 30 canvassing and entire square block, knocking on doors and ringing door bells.  Is this something they must do to become a member of that cult? BTW, there has never been any person that could demonstrate that he/she is god. It sure is an invented religion, and so are all religions; yes Christianity surely was invented.

Yes.

And that is not true of every religion.  Buddhism and Taoism, for instance, have no problem with practitioners having more than one religion.

Polytheistic religions generally consider that they may not know all the gods, and that others may have other gods.

Virtually every religion believes that. However, there was only one founder of a religion Who clearly demonstrated that He was God, by constantly doing things only God could do. That was Jesus Christ, Who founded one Church, said it was to remain one, and promised that one Church the fullness of God's truth until the end of time. All other religions and denominations are just manmade organizations that teach the beliefs of their various human founders.