MoST explicitly mentions Kirk's first command to be a "Destroyer Class" vessel which would put a Miranda Class vessel ("Starship Class") out of the game.
To be sure, we have never seen a
Miranda associated with the "Starship Class" moniker: there are no TOS style dedication plaques to that effect, no onscreen sightings of TOS style
Mirandas, and if we venture to fanfic/speculation, we could just as well decide that the putative TOS
Miranda dedication plaque would actually read "Frigate Class"...
On the other hand, since there has never been an actual destroyer class starship in onscreen Trek, we don't know what sort of ships might fit that category. The closest we get are fuzzy images on some TOS movie screens, not really identifying Franz Joseph's single-nacellers as destroyers, and completely up-in-the-air verbal references to Starfleet-operated destroyers in the battle of "Sacrifice of Angels".
USS Lydia Sutherland, pardon me, sounds weird, especially since it is known that two Horatio Hornblower ships were mixed together here.
...And anyway, I think McIntyre specified that ship as having been a "great little cruiser". So if we want to insist on the idea that Kirk's first independent command was a destroyer, then this ship lost at Ghioghe is not it.
As for multi-part names, we don't know exactly what the full name of a verbally introduced starship would be. Picard might mention offhand the
Nobel, but the hull of that unseen starship might actually read
USS Alfred Nobel; Shelby might gasp that the
Chekov was lost, but the pennants might say
Anton Pavlovich Chekov...
Timo Saloniemi
