Just because they move doesn’t mean the name will change. There’s plenty of teams, especially football teams with their larger stadiums, that don’t actually play in the city of their name. Heck the New York football teams don’t even play in the same STATE as their name.
When the LA Rams left the Colisseum to move to Anaheim, they were still the LA Rams.
The NY Jets and NY Giants play in East Rutherford, NJ.
Cowboys Stadium is in Irving Texas.
And I think the Oakland Raiders play out of a moving van!