As a means of being sufficient/distinguishing/key to identifying it,yes but it tells you nothing more than that. The issue is that you gave already stated that your axioms that humans exist and are moral agents ate universal so they too form part of this base of a set of beliefs.
Believing in the existence of god or gods is a
necessary requirement for agreement with a theistic moral philosophy, it is not a sufficient requirement.
Believing in the existence of humans and that they are moral agents are
necessary requirement for agreement with humanism, again they are not sufficient.
The difference being that those initial
necessary requirements for humanism are almost universal, the
necessary requirements for a theistic moral philosophy are far from universal.
And while humanism is currently (particularly in the UK) seen as being non religious, this is a narrow interpretation and throughout history, and today, there are those who clearly see themselves as Christian humanists, Buddhist humanists, Muslim humanists etc.