[untog]

you can't deal with those situations when you're implementing something that's actually anonymous

True, but this login isn't "actually anonymous" - but I can't think of a better term so I don't blame Facebook for using the one they did. It's effectively a global ID with no data attached to it.

[thinkling]

Pseudonymous is the term you're looking for, I think. An identity that's not tied to your real-world identity.