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!
The Miami Dolphins (and starting next year the Miami Hurricanes) play in Dolphin Stadium, which is just inside Dade County from Broward County.
The Washington Redskins play in Landover, Maryland.