I'm from NYC and call it "plain" or "cheese." "Regular" makes me think too hard as to whether the "New York thing" is to say "regular" or "plain." It's also a lot of syllables.

A similar phenomenon occurs with waiting "in [a/the] line" vs "on [a/the] line." I think I say either, but I'm "supposed to" say "on line."

I've always called it a plain slice but I've heard regular/cheese/plain used interchangeably

I grew up in NY and lived in NYC and I still call it a plain slice.

when you order, it's called "a slice".