Starfleet was of the Terran Empire though...and the entire point of the Commonwealth was to establish its self separately and create something new, so I think they'd probably come up a new name for their naval fleet. Starfleet would have overtones of the Empire IMO if they used it.
That's entirely possible. On the other hand -- how many people are bothered that the German air force is still called the Luftwaffe
? It's possible that the term "Starfleet" is considered a generic term for space services, no more objectionable than "Luftwaffe" in German, or "Air Force" in English.