These are my suggestions for new promotion names for the bombard/marine unit lines:

Marine: the same, but without the "marine" designation

Bombard:

Naval Bombard vs. Naval Units -> Firing Solutions (better ballistics and targeting of moving targets, such as ships)

Naval Bombard Extra Movement -> Engine Crews (only name I could come up with that's non-specific of any engine type - coal, oil or nuclear)

Naval Bombard vs. Land Units -> Airburst Shells (don't know if they were ever used on naval artillery, but what the hell)

Naval Bombard vs. Districts -> Broadsides (this is a generic engagement tactic, but concentrated fire is particularly useful against hardened targets)

Naval Bombard Heal Outside -> Naval Logistics

Naval Bombard vs. Air Units -> Fast Tracking (pertains to AAA cannons, but could also refer to CIWS or Standard missiles for the more modern vessels)

Naval Bombard Extra Attack -> Autoloading Magazines (self-explanatory, really)

EDIT: also, the Civ V battleship model can't come soon enough; the one from 6 is an absolute chonk lmao