Bud Adams and Art Modell changed the names of their teams after they switched cities. Adams, however, retired the name Oilers with the NFL's blessing, while Modell had to give up the name Browns as part of his legal maneuvering to flee Cleveland. Cardinals owner Bill Bidwill moved from St. Louis to Arizona and kept the name. It has been in his family since his father owned the Chicago Cardinals. The Cleveland Rams became the Los Angeles Rams, who became the St. Louis Rams and won the last Super Bowl.
Some teams have strong nicknames and weak logos.
Others have good logos and bad nicknames. In the case of the Houston Texans, owner Bob McNair chose a name that encompassed an entire state. Texas is such a diverse state, and that diversity is something that makes it so great. We didn't want anything that could have a negative image. We didn't want to take a chance on having a name that could cause people to take offense.