Aah, somehow I read your earlier statement to mean H&C & Santa Claus were the same.

And you're absolutely right, Santa Claus is one person, and the name signifies it is the same person.

Looks like Harry told Quirrell that it was signed Santa Claus - we should assume in the future letters are from the same person or Q, since Q would definitely forge such letters if it was to his advantage.

"Although of course Harry hadn't told Professor Quirrell who'd sent him the card, nor what it was supposed to do, before he'd asked Professor Quirrell if it was possible to tell where the portkey would send him." ... Harry had shown Professor Quirrell the note that had accompanied the deck of cards, saying nothing of the earlier notes.

My hypothesis for now is SC = Dumbledore/Nicholas Flamel. H&C = Quirrell.

And 75th above makes a strong case for SC=D - http://lesswrong.com/lw/ams/harry_potter_and_the_methods_of_rationality/60uj