Met in RL, adds you on Facebook at first possible chance, what do you prefer to do?

I know there is a lot of facebook posts on here but they mostly seemed revolved around game on facebook, this is more geared towards proper amounts of privacy, accepting or ignoring friend requests.

Several times now I've gotten numbers, play some game in person or via texts, and things go alright, some successes some failures, but in two recent instances the girls eventually find out or ask for my last name. Immediately thereafter they send a friend request on facebook. Its actually kind of frightening how quick it happens. I've got their number so I don't need facebook to talk to them and facebook comes with lots of downsides (and upsides I suppose).

Against my instincts I accept them, usually, which I always regret (at least at that time). I feel accepting them betrays some mystery about myself and gives them too much access to my life without working for it. I've been debating whether to do nothing (leaving the request in the inbox), flat out ignoring the friend request (decide whether to accept at a later date), or accepting but under heavily restrictions (which gives an IOI to her but retains some mystery). And obviously I've been thinking about significantly delaying coughing up any last name lol.

What do you guys find you have most success with? Or have strong feelings any one way?

Cheers.