Now & then I see friends putting a false family name on their Facebook profile. While I respect that decision, I don't think it's really a productive idea. Maybe you can give me some hints I am missing.
My point in short:
Your family name isn't what's valuable to FB. What's valuable to them is what you write and who you connect with. If you don't want FB to spy you you shouldn't be here in the first place, because your data usage is what matters. By having all your communication, they know where you live, where you friends live, probably how old they are, what all of you are studying, who are you best friends,...
Place yourself as a car dealer. Does it really matters if your customer is named Smith or Johnson? Doesn't it matters more to know that he's a lawyer or that he's going to the Golf club? Now that may be some clue on how much he can invest on a car.
Well, you may fear that strangers try to sneak information about you that should stay in your friend circle, and you're probably right about that possibility. To protect yourself against such thinks, review carefully your privacy settings.
So if you fear Facebook spying on you or using your data, maybe you shouldn't go there at all - or at least reduce your usage to the minimum. And review your privacy settings, it can't hurt.