If you don’t want to give them personal information such as your last name they have no business seeing your Facebook profile.
It might be a way for them to gather personal information from you without asking you directly.

I personally don’t even give my first name to people online unless I feel comfortable doing it. If you feel even a little bit uncomfortable giving information about yourself to those guys, DON’T DO IT. Sorry for screaming but you need to realize that there is a reason why you feel uncomfortable about it. If you keep contact with them on the dating site only it will be easier for you to “cut the cord” if things turn bad at some point of if they turn out to be stalkers etc…

I would keep the dating and facebook network separate for privacy purposes. Just tell them you don’t have one. The only time you give them information like this is when you actually end up in a relationship with one of them for a decent amount of time, and knowing that you can finally trust that person. But these are people you never even met in person.