What do you call the number of atoms in a molecule?
The "number of atoms"'s name is... the number of atoms. I am not aware of any special word for that. Databases may not let you search/filter that kind of criterion, i.e. the total number of atoms, but usually let you search by "chemical formula" which is, in your case, C2H2O2.

I have just tried with Chemspider by typing "C2H2O2" in the search box and it disappointingly gave me just 3 results, i.e. glyoxal (OHC-CHO, not in your list), 42879-41-4 and 16005-17-7.

DID YOU KNOW? Just to expand the scope, did you know that the last digit in CAS# is actually a check digit? It helps any software checking that you did not mistyped the number.