Atomic mass number and mass number in atomic symbol
The IUPAC preference for A in $\ce{^A_ZX}$ is mass number. The term would also apply to a molecular fragment, for instance in a mass spec. So depending on the context atomic mass number or molecular mass number might be used to be more specific. 

The problem with you arbitrarily defining A in $\ce{^A_ZX}$ as atomic mass number is that various references might just use mass number. So depending on context you'll need to be able to decide which possibility is the correct one. Of course in spite of IUPAC definitions there are no doubt multiple variations in the past and current literature.