It's harder to answer the question "If you don't believe in a certain "God" are you an atheist.

That can be approached from two perspectives. One, from within the ranks of those who do believe in that God, and from outside that group.

The former could well believe a person is an atheist even though there is a strong belief in their own "God", thinking that belief in a false god is the same as believing in no "God".

And from outside one might be more tempted to believe that they were not an atheist if they believed in any "God" or "Gods".

Therefore, atheist is a relative term, at best, and not really definitional unless one clarifies it - "I believe man is the be all and end all, and there is nothing besides man, and other plants and animals." That would define an atheist clearly. Otherwise it can be murky.