Actually there is a place/village/oasis in U.A.E. named Manama as well: MANAMA (Dependency of AJMAN)
so i guess "Manama City" is sometimes used to prevent mix-ups...
After extensive internet research I found only one reference to Manama City. I guesss one could also say Paris City or London City, but the fact remains that the oficial name of these cities does not include "city."