looks like a type of back rank mate. I don't think the specific pattern with a pinned rook has a name.
Named?
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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
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