I always thought it was a pretty obvious reference to the face of Voldemort hidden behind Quirrel's head. It could also refer to Snape's hidden heroism, which was first hinted in that chapter. I don't think it was Dumbledore. His secrets don't get revealed until ages later. Or am I forgetting something?

Ah...but just because his secrets weren't revealed until later doesn't mean he didn't have them in the first book.

I'm just thinking the revelation was too far in the future for it to be referred to at the time. It isn't like foreshadowing something in the actual plot - a chapter title is too subtle for that.

But, in retrospect, didn't Dumbledore have two faces figuratively?

That's true. I just don't think that particular chapter title was a meant as a reference to the revelation, so many books in future.