Why does Facebook as my dummy account if it knows people I don't know?

Due to the nature of a couple of games on Facebook, (at certain points you either need to get some of your friends to give you a “ticket” or you have to pay cash), I have created a couple of dummy Facebook accounts, as I’m not paying and not bothering my real friends. Both these accounts have just 1 friend, me, and have never interacted with anybody. However Facebook’s email “Hi X do you know Y” frequently suggests Ys that I have no idea who they are. Why, in these circumstances would Facebook suggest friends that I’ve never heard of?

Facebook is secretive about the algorithms they use, but I suspect those people have searched for names similar to your fake names.

Just a guess:
if you play a certain game a lot, could Facebook be matching you with other people who play the same game?

It’s matching you to anyone it can. If you have no obvious friends it’s going to use less accurate algorithms. There are lots of ways of matching you to people you’ve never met, even random, just to get some traction.