It hit me this morning that since recognizing my atheism (many moons ago), I've actually become a much more "moral" individual. Perhaps it's simply a case of age-related maturation. You tend to act much less impulsively and think things through more. Or maybe, once I eliminated the fallacies of belief, I became more acutely aware of what really constituted ethical (moral) behavior. Maybe since I knew that there was no "forgiveness" to be obtained, I just had to behave better, to be a better version of myself, so I could be at peace with my choices.
I've never been all that concerned with the judgments of others, so what anyone else thinks of me is rarely a consideration or motivation. BUT, I need to be able to face myself. Every day.
Call it "conscience", or whatever you choose. Mind you, this is all happening in MY head. Your mileage may vary.