On the subject of class naming. If two ships are identical, but the missions for each ship is different, could they be named to two different classes?
That depends on your definition of "identical", I guess. Take for example the
Niteroi class frigates of Brazil. Seven were built by Vosper Thornycroft to their rather modular Mk 10 specs. All had the same hull and engines. But four were equipped for anti-submarine warfare, two for general purpose warshipping, and one was a dedicated training ship without armament or sensors. Calling the GP variant the
Constituição class or the training ship the Brasil class is a matter of taste; the Brazilians themselves don't do that.
In contrast, the
Leopard (Type 41)and
Salisbury (Type 61) frigates of the Royal Navy were similarly identical hulls with dissimilar missions, and they definitely received separate class names and designations. The
Kidd,
Spruance and
Ticonderoga classes of the USN were again nearly identical except where it counts, that is, the weapons and sensor suite, and the
Tico was even called a cruiser while the two identically sized sisters were destroyers.
If two starships of the same design are given different missions, do they differ from each other as much as those real frigates (completely different guns and radars on the same hull)? Starfleet has the technology to achieve that, perhaps even at the push of a button, and it could all be internal, leaving us poor watchers high and dry. OTOH, does it matter? We don't have canonical dialogue examples of the same starship class being called by two different mission designations, but we can
see ships more or less identical to
USS Reliant perform missions called "supply ship" and "science vessel" plus an unnamed mission that amounts to frontline combat. We just can't tell for sure whether they all are known as the
Miranda class while in those differing roles. (Indeed, we never hear
what class these ships might be -
Miranda is pure backstage, never mentioned on screen or used in an in-focus Okudagram that would connect it to the design.)
...All in all, the answer to the question as regards Starfleet naming practices is "we can't tell", at least not yet.
Timo Saloniemi