The general notion of deism does indeed tend to include the idea that God does not interfere with the universe. However, it's also basically the best word we have for the idea of someone who believes in God, but who arrived at that belief through reason and logic rather than belief in supernatural revelation, and who rejects the core beliefs of all official religions (besides the existence of God, of course).
Theism?
I believe that the usual definition of theism includes no such rejection of supernatural revelation; a follower of a religion would be a theist, but not someone who simply believes in God due to logical deduction or extrapolation.