looks like a type of back rank mate. I don't think the specific pattern with a pinned rook has a name.
Named?
Sort:
I agree with Borg Santa. I just checked my Silman Complete Book of Chess Strategy, which lists fourteen "named" mates, but didn't see that one. What your position/mate is closest to is "Morphy's Mate," but that involves a direct check from the bishop on the a2-g7 diagonal.
If it hasn't been named yet, maybe you can name it. Something catchy, like the "Prelate Piledriver" perhaps...
Cheers,
Becky
Call it a "Clever Cavalier's Mate". 
"Cavalier's Mate" sounds acceptable as well. But not with the sign "?!" for a dubious move. 
Well, seeing how it's an old, common checkmate, Cavalier's Mate doesn't work. Another problem is the lack of a knight!
Won't argue. I know better than to resist.
Does this checkmate have a special name, or is it just a back rank mate?
A friend of mine once said that after 2... Rf8 3. Bxg8 Rxe8, black's rook had free range to harrass white's king. :-p