With the signing of Nakajima, I checked out his Japanese team and discovered that it is named for the company that owns it, i.e.: Seibu Railways. Several other teams there are named for their ownership, including:
Hanshin Tigers: Hanshin Electric Railway Company
Nippon Ham Fighters: Nippon Ham (food processing company)
I guess if that were the case in MLB, we would be the GAP Athletics or maybe the Fairmont Athletics. Also, the Tigers would be the Little Caesars Tigers.