Allrighty. Just a few I can think of off the cuff:
- Obviously, the OG Final Fantasy Tactics. You can name units you hire, and I think have one opportunity to rename any units you persuade when you get them. Neither of the Tactics Advance games allow any sort of naming, though.
- Tactics Ogre: Let Us Cling Together and Tactics Ogre: Knight of Lodis allow direct naming of hired troops. Of the 4(!) versions of LUCT, the most recent remake (Reborn) is the only one that gives a single opportunity to rename units persuaded in battle, when you're deciding if you want to keep them afterwards.
- Pretty much every single strategy game from Nippon Ichi (Disgea, Phantom Brave, Soul Nomad and the World Eaters, etc.) allows naming your generics, though I don't recall if you can change it after hiring them.
- Phantom Brigade is a somewhat NuCom styled mech tactics game, whose combat mechanics are a strange blend of real-time and turn-based: all units on the field act concurrently in five second chunks, and you have to coordinate your team by timeline rather than using grid squares or time units. I found it difficult to wrap my head around, even before I noticed it allows they/them pronouns for its pilots.
- The somewhat recent Battletech game (2016-ish, I think?) also lets you customize your non-important pilots, with the same pozzed caveat.
- Wartales is a low fantasy cross between NuCom and Mount and Blade, and allows you to change anyone's name at just about any time you're not in battle, even the few static characters you can pick up.
- Symphony of War is a mix of Fire Emblem and Ogre Battle: March of the Black Queen (if you've played the aforementioned Soul Nomad, it's very similar) that lets you rename just about anyone in your army between missions.
- Fell Seal: Arbiter's Mark is another FFT-type that allows naming hired generics. I think it allows renames after the fact, and you can even load custom portraits for your characters.