That is what the original X-Force
was, just the continuation of The New Mutants
after that series ended at issue 100 with (bad) Rob Leifield art. IIRC, the editor at the time said that the change was made because any team that lasts 100 could hardly be considered "New" anymore.
The name has been used for several other teams and concepts, especially in recent years. X-Force was the name of both of the Wolverine-led wetworks teams. Both the team sanctioned by Cyclops and the team that Wolverine kept secret. Currently, there are two teams using the X-Force--Cable and X-Force
and Uncanny X-Force.