Team name changes while in the same city:
Boston Braves: Were also called - Red Stockings / Beaneaters / Doves / Rustlers / Bees
Boston Red Sox: also called - Americans
Chicago Cubs: also called - White Stockings / Colts / Orphans
Cincinnati Reds: also called - Red Stockings / Redlegs
Cleveland Indians: also called - Blues / Bronchos / Naps
Houston Astros: also called - Colt .45's
Brooklyn Dodgers: also called - Atlantics / Grays / Bridegrooms / Grooms / Superbas / Robins
New York Yankees: also called - Highlanders
Philadelphia Phillies: also called - Quakers (and Blue Jays, according to WIS)
Pittsburgh Alleghenys: also called - Alleghenys
St. Louis Cardinals: also called - Brown Stockings / Browns / Perfectos
and of course, Tampa Bay dropped the word "Devil" from their name a few years back.
Granted, the two most recent of these changes were in 1965 (Colt .45's to Astros) and 1960 (when the Redstockings went back to being just the Reds), but it shows that it can and has been done before.