Both are correct. In general, American English tends to prefer 'take a..' in all verb+noun combinations such as this, while British English tends to prefer 'have a...' or 'go for a..'. But otherwise the two phrases are interchangeable.

SuKi is correct, and as a language learner treat them as interchangeable. Interestingly, more as a comment to other native speakers, I think I might use them a little differently. I'd use "take" if were describing what I was doing or was asking a question to someone. I'd use "have" if I were describing what a baby or child was doing.

One in the same. Either is correct. I would say that to take a nap is a little more relaxed in it's tone.

I would use both. I don't know which I use most often. I just say whichever feels natural at the time.

In the States, we use "to take a nap." I don't think I've heard anyone use "have" for naps here, but I may be wrong!