In my outfit -
Prior to V1, the PNF calls out the problem in the clearest way he can...
"Engine Problem"
"Aft Cargo Door"
"Cargo Fire"
and the Captain will call "STOP" or "GO".
After V1, PNF still calls the problem eg:
"Engine Problem"
PF need not say anything... just continues the takeoff.
Old Smokey certainly has some valid points about saying nothing. The PF is ready to hear "V1... ROTATE" in that order. In some incidents they have realised that when the PF speaks after V1, the PF sometimes rotates, even if he has said Engine Failure and it is well below V1. Shouldn't happen, but when everyone is keyed up and adrenalin running, it does.
On the other hand, the aircraft I fly uses a different rotate rate and initial pitch attitude for an engine failure. It is nice to know why there are control issues, rather than guessing if it is an engine problem or losing a number of tyres.
We all just follow SOP's and try not to hit anything