In My Traveller Universe, Imperial Basic is the main written and spoken language of the 3rd Imperium, derived from Solomani Basic (also known as Galanglic) with Vilani loan words and grammatical borrowings. Due to the vast size of the Imperium, and the relative slowness of communications, Imperial Basic has evolved several distinct regional dialects and accents.
Within my Traveller Universe, the RimWorlds Sector, most subsector populations have a distinctive accent and form of Imperial basic, though these dialectal groupings may spill across subsector borders along stellar mains or through clusters.
While transfers of popular media through trade might tend to act as a unifying agent when it comes population language accents, such transfers are unlikely to take lasting root amongst populations numbering into the billions. The effect would be akin to, say, fans of London gangster movies adopting a faux-East-Ender accent amongst themselves, but reverting to their native New Zealand twang when communicating with people outside their social interest group.
Playing around with dialects and languages can add an extra dimension to your players’ immersion in your Traveller campaign – reminding them that, in their imaginations, they are a long, long way away from home.