Would a imperial mithra keep normal naming conventions pre stormblood.

[Cilia]

Conquered people we've seen adopt the Imperial lifestyle typically keep their forename, use the Imperial title "middle name," and have a Garlean surname (e.g. Asahi sas Brutus, Fordola rem Lupis, Grynewaht pyr Arvina, etc).

Defectors tend to drop their title "middle name" after leaving Imperial employ (e.g. Cid Garlond, Gaius Baelsar). Imperials occasionally refer to them using this previous title (i.e. some Imperials still call Cid "Cid nan Garlond," like Nero during the Praetorium) but given they no longer follow Imperial orders it's not necessary.

Garleans Imperials tend to be racist toward non-Garleans, so they'd be treated as second-class citizens regardless, and could only reach "sas."

The racial naming conventions and culture just describe peoples in their "natural" habitat, such as living in exclusive race / tribe societies. Peoples outside of those don't necessarily adhere to their cultural traditions.

... and this isn't XI, so there are no Mithra beyond a Wind-up toy from Eureka. They're called Miqo'te here, or Mystel on the First (and actually have playable males!).