I would say it's "regex", this is based on my own experience, how I've heard it, and the community discussion here.

I can't find it at the moment, but this discussion was on meta over tags on SO, which is why this is the only question tagged "regexp", the rest (8441 and counting) are tagged "regex".

Just a side thought here: does it matter which is "correct?" Think about the purpose here, why do you use any word? To communicate. To a certain degree, it doesn't matter what's correct or not, it matters which one you can effectively communicate to more people. I would say you could easily argue to use an incorrect term, if that's what the majority of your audience uses, since communication is your goal.