Cincinnati would be a rival with Cleveland and Pittsburgh would be a rival with Philadelphia.

I would name the Cincinnati team the Cincinnati Stingers and name the Pittsburgh team the Pittsburgh Pride.

Some NBA trivia:

The Atlanta Hawks used to be the St. Louis Hawks.
The Sacramento Kings used to be the Kansas City Kings.
The Utah Jazz used to be the New Orleans Jazz.
The Los Angeles Clippers used to be the San Diego Clippers, and before that they were the Buffalo Braves.
The Brooklyn Nets used to be the New Jersey Nets.
The Memphis Grizzlies used to be the Vancouver Grizzlies.
The Oklahoma City Thunder used to be the Seattle SuperSonics.
In the late 1990's the Washington team changed their name from the Bullets to the Wizards.