...Which sort of relates to the prime reason why two identical ships may belong to two different classes: their class names were given by their two different operators.
Spruance, Kidd and Ticonderoga can be distinguished from each other simply by looking at the silhouettes. The American, British, Canadian and Australian versions of a common destroyer or cruiser class in WWII often could not, either because the exteriors were identical, or because every last nut and bolt was. And pre-owned warships further stir the cauldron: ex-USN Garcia or Perry frigates currently serve under a dozen different class names across the globe.
Starfleet probably is too much of a unified body to assign multiple class names to identical ships for mere organizational subdivision reasons. That's not completely impossible or unheard of, though: the medical ship in "All Good Things..." says Hope class on the dedication plaque, while the Encyclopedia suggests that an identically shaped (unseen) vessel in "Interface" was of Olympic class instead. I could easily see Starfleet pulling aside a few Olympics, giving them medical innards, and renaming the variant Hope class.
Then again, even unified bodies can give multiple class designations to what is basically a single design. The Royal Navy mass-produced destroyers before WWII in batches of 8+1. Each batch was named after a letter of the alphabet, so e.g. the A class had eight identical ships with names beginning with A, plus a ninth, larger vessel for flotilla command that was still considered part of A class but didn't follow the alliterative naming scheme. The B class was completely identical to A class, but nevertheless considered separate. C class went to Canada wholesale and was locally considered part of the River class, combining select ex-RN destroyers from multiple "letter classes" and renaming them after local rivers without any alliterative ambitions. D class introduced various improvements, while E and F were further modified but identical to each other. And so forth until I class... During the war, the RN also built a new C class when it ran out of letters, and divided it into four subclasses of eight: Ca, Ch, Co and Cr, with alliterative names on those first two letters. If you can still follow, be relieved that Trek fandom has only come up with a fairly simplistic class/subclass/variant name scheme so far...
I could see the Miranda family as a close analogy to those British destroyers. Initially, there'd be just a couple of batches, like the ones suggested by Todd Guenther in Ships of the Star Fleet; each batch would have its own class name, whilst there'd be some design variation between and within the batches. Further batches would be built in the late 23rd and early 24th centuries, some possibly still given separate (sub)class designations - but at some point, Starfleet would stop caring, and would simply retroactively name all the slightly different ships Miranda class collectively, perhaps after the name of the first or latest ship/batch in the general family.
Timo Saloniemi