I'd think if they were a straight purchase from Russia, they'd get called Fulcrum anyway.
If they were British license built, I think you might see it get some sort of official name suitable to a British combat type. Perhaps an aggressive weather pattern that reflects the types Russian origins, like "Blizzard".
There is also scope for predatory names as well. The RAF had Jaguars so who's to say they can't have something like a BAe/MiG Leopard?