No offense intended, but can we just forget about the name thing? I'm sure he doesn't care. If you translated my name into Russian using cyrillic characters, it could come out about half a dozen different ways, and I wouldn't care which one got plastered on the back of my Moscow Dynamo jersey. Really, it's meaningless. Call him Kastsitsyn, Kostitsyn, Kazzy, AK-47, whatever you want, and we'll all know who you mean.
(Is it true that we've just never had a Russian on the roster before whose name wasn't so simple? Wow. Seriously, as the native Russians here are saying, and I'll chime in from my university days of studying Russian, you can chose to spell it a variety of ways using our limited alphabet, and none of them is intrinsically right or wrong.)
Probably the NHL will adopt an official spelling based on his contract (if they haven't done so already based on his draft), and that'll be how he gets spelled in the NHL, but there is no right or wrong absolute answer.
I asked my fiancee, who was born in Russia and lived there until she was 16, about his name. i showed her the cyrillic spelling. She said that in Russian it is pronounced Kastsitsyn; in the Belarussian language the "o" is stressed and is therefore pronounced "Kostsitsyn".