I don't know about searching names but if you're not friends with someone, you can pay $1 to send the message to the person's inbox instead of "other" folder.
So, if someone pays, I cannot hide from them? Ugh... Facebook sucks
Well, they can find you even without paying, but only message you as a friend if they pay.
I actually got a survey link a week or so ago from Facebook wondering how well they were serving their customers. I blasted their privacy (or lack thereof) options. I'm doubting it will make a difference, though.
I changed my name of Facebook to a shortened version of my first name and my middle name. I also changed the Facebook URL to remove my last name so it wouldn't come up on a Google search. It seems to be working.