There is no specific collective name that refers only to the molecules H2 and O2. The only thing they really have in common is that both molecules are composed of two identical atoms. Thus, we can identify them as belonging to the category of diatomic elements.
The term "diatomic" is simply what it sounds like; two atoms, meaning that the atom will not be found by itself (monatomic) under normal circumstances because of its reactivity. Part of the reason for this is that the atoms, being identical, also have identical electronegativities, and therefore the electrons are equally shared between them in the bond. This isn't to say that alternative bonds are impossible, such as a single oxygen bound to a single fluoride atom, but that the electronegativity difference in these atoms causes the bond to be more energetic, and therefore less favorable, and less stable. It would also be impossible to satisfy the octet rule for this arrangement, further lending to its reactivity, and improving the relative stability of the O-O and F-F arrangements.
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