Can you have two accounts on Facebook with two different names?

Yes

Facebook requires that your account be a real person. While its possible to do, if you are caught your accounts will be removed.

Why would you want to do that in the first place. I can think of no valid reason to do it.

While you could do it, why are you wanting to, what is your purpose?

It isn't for me. I think someone I know has two accounts and was wondering if this was possible

A person can have a business account, but then you would know what the business is.

P.S. Please don't use PMs to provide follow-up, just post to the thread.