How do covalently bonded atoms (molecules) have an electrical charge?

Covalently bonded compounds are neutral compounds and do not carry any charges. Can you provide an example of a covalently bonded compound that has a charge?

You terminology is somewhat confused. Chemical bonding has to do with transfer or sharing of electrons - not atoms. You statement: "No atoms are gained or lost, atoms are shared in a covalent molecular bond" should read - No electrons are gained or lost, electrons are shared in a covalent molecular bond. It is for this reason that there are no charges on purely covalently bonded molecules.

Edit after additional information:

You are being confused because, for instance SO4 is not classifies as a self standing molecular compound . It is classified as a radicle or an ion . The sulfate ion is a polyatomic anion with the empirical formula SO4 2−. It consists of a central sulfur atom surrounded by four equivalent oxygen atoms in a tetrahedral arrangement. The symmetry is very similar to that of methane, CH4. The sulfur atom is in the +6 oxidation state while the four oxygen atoms are each in the −2 state. There is an imbalance of charges, in total 8- and 6+. The sulfate ion therefore carries a negative two charge. This 2- charged ion cannot exist on its own, and has to be ionically bonded to a positvely charged species, such as 2H+ in sulphuric acid, H2SO4 ( neutral charge on the complete molecule) or Mg2+ in MgSO4 - also neutral charge on the complete molecule. As you know in aqueous solution these compounds dissociate to form the respective positive and negatively charged ions. But in the pure state, say MgSO4 as a dry powder salt, there are no ions produced, so no charged species exist. It is not possible to produce a covalently bonded compound called SO4 which carries a negative 2 charge.

Exactly the same thing applies to NO3 - and PO4 3- There are covalent bonds, but these are not compounds.

The existence of a hundred percent ionic or covalent bond represents an ideal situation.

In reality no bond or a compound is either completely covalent or ionic. In case of a heteronuclear molecule like HF, the shared electron pair between the two atoms gets displaced more towards fluorine since the electronegativity of fluorine is far greater than that of hydrogen. The resultant covalent bond is a polar covalent bond. The distortion of the electron cloud or the shift in the electron cloud towards the more electronegative atom leads to a partial positive charge on the more electropositive atom.

Its ionic bonding while it dissolves in water somewhat merely dissolving as HCl molecules It types hydrogen and chloride ions so its quite ionic because of the fact it dissasociates. Hydrogen could have covalent bonding in organic and organic compounds the place they do no longer dissasociate like in alcohols