This may work for custom leagues than standard leagues but how about a city relocation offer that your team gets instead of changing your city's name to your liking .

1. For example : Like Washington Redskins get a City Relocation offer from Baltimore , Dallas Cowboys gets a city relocation offer from Houston , etc.

then once you get that offer you have to compare the PROS and CONS of both cites.

Like how money the move will be , how much the stadium will cost , etc. for both cities then either accept it or reject it like you do now for trades for players and/or draft picks.