What is the peak of coffin corner called?
Yes.

The peak is the actual coffin corner. That's why it is called a corner.

In the coffin corner the aircraft cannot climb any higher, which is a definition for the absolute ceiling. Going any faster will reduce L/D and cause the aircraft to sink; that Mach effects are involved is of minor importance. Going slower will also decrease L/D because the aircraft is approaching stall.

What is special about the coffin corner is not the corner itself, but what happens when the aircraft gets too fast: Now stronger shocks will increase drag and decrease the maximum lift coefficient such that the aircraft is locked into a shallow dive from which it is initially not able to recover. Going too fast while flying at the "regular" absolute ceiling merely means that you will lose some altitude but not lose control.