I’m curious if there’s a name to the belief I have. I wouldn’t exactly call it atheist, though i generally lean that way, but I wouldn’t call it non-theist. The thing is, I just plain don’t care if God exists or not. They could, or they couldn’t, it really has no bearing on how I live my life. For that reason along I think I go in the atheist camp, but I always thought that was used to describe people who don’t think he exists.
Not the answer to your question, but I find it important to point out, that atheist and non theist are not necessarily the same.
A non theist isn’t necessarily a non believer who rejects all religion like the general understanding of an atheist.
The Dalai Lama for example calls himself an non theist and so do I as a Buddhist. Buddhism is a believe system, a religion, that does not believe that there is a god or gods. Some subdivisions of buddhism believe in divine beings you can turn to and pray to, but they all used to be ordinary humans, same as the Buddha, who obtained enlightenment and transcended into a higher form of being.