Why does the French Open have two names:  French Open and Roland Garros ?

Many sporting events are known by the global media by names that differ from their "official" native titles.  The best-known example of this is probably The Open Championships in Britain....which is known as "The British Open" around the world.

The official French language name for the tennis event is "Internationaux de France de Tennis."  "The French Open" is the name used by the foreign and English-speaking media.

"Roland-Garros" is used in France and the French-speaking media as the "shorthand" version of the event, in much the same way that the race known as "24 Heures du Mans" is commonly known as "Le Mans."

Fun fact:  The venue is named after a person named "Roland Garros"...but French language rules specify that event names based on a person's name be hyphenated.  "Roland Garros" can therefore refer to the person or the venue, but "Roland-Garros" refers specifically to the event itself.

Roland Garros is the popular name the French people and the tournament calls itself. Everyone in France call it Roland Garros. So if you buy a souvenir, it will say Roland Garros

 rather than the official name “Internationaux de France de Tennis.” French Open is the unofficial name English speaking people give it. 

aus open is called 'down under' and the us pen is called  'los mess' as well as 'flushing meadows'

(The stadium and tournament are both hyphenated as Roland-Garros because French spelling rules dictate that in the name of a place or event named after a person, the elements of the name are joined together with a hyphen.)

Venue: Societé de Sport de Île de Puteaux, at ...

Surface: Sand – outdoors (1891–1907); Clay – ...

It's named Roland Garros after the stadium where it's played.

Roland Garros is the place, the French Open is the tournament. 

Roland Garros is the name of the stadium, not the tournament.