Rewatch the scene where La’an enters the bridge, and keep an eye on the dedication plaque to the left of the turbolift.

It identifies the ship as the UEF Enterprise.

“Kirk claims never to have been to Earth at all, having been born in space on the USS Iowa. His counterparts were born in Iowa, USA, in the Prime Universe 2333 and on the USS Kelvin in the Kelvin Timeline.“

Alt-Kirk’s ship is identified as the UEFS Enterprise when La’an first enters the bridge, but I also heard his place of birth as being the USS Iowa.

Does that imply that humanity has multiple military space fleets? Or maybe that unification of Earther’s governments didn’t happen until after Kirk’s birth in this timeline?