"Is there a name for black's 23 move?"
it is called 23....Re4
jb70 has it spot on a Deflecting Sacrifice. The White Queen is deflected from defending h3.
23....Re4 24.Qxe4 Qxh3 mate.
You are correct White is not forced to take e4, I bet he was expecting 23...Rec8
and too quickly dismissed 23...Re4 as an error, though his position is still very bleak.
Two things to note.
Black played 13...Bxc3 here. Always a dodgy move taking a c3 Knight with a g7 Bishop
especially if, as here, White still has their DSB on the board. White could have played
14.dxc6 which gives White all the winning chances. Black I'm sure will have to give
up at least the exchange for the c6 pawn after cxb7.
Back to the mate.
In that set up a Rook on h3 also mates. There was no way of forcing it in
the actual game but a handy mating pattern worth knowing.
sbacat - wadanz RHP 2016