I think "Starfleet" is a pretty darn generic name for a fleet of starships. And
according to the OED, it's been used in other works of fiction besides
Star Trek, and while ST popularized the term, there's at least one documented use of "star fleet" preceding ST, from a 1939 story by Lester Del Rey.
Besides, at the time the Commonwealth comes into being, the Terran Empire's been extinct for over 85 years. I think more people would remember the tyranny of the Klingon-Cardassian Alliance by that point.