
This lore page on Othard suggests that Doma had no regular contact with Eorzea (or anywhere outside Othard) at all until two decades ago, so it seems highly unlikely to me that the two would share a basic language.
Sticking with my "Common is a trade language; Doman still exists as a local language" theory.
Edited to elaborate: Like 20 years is still a decently long time to integrate a new language into society if it's useful enough, but I also don't think it's enough time for the old language to totally die out. Othard's cultures were isolated for centuries; they will have developed language families, dialects, and all the related oddities independent of anything an Eorzean would be familiar with. Even if the two Hyuran populations either side of the mountain-range began with the same language, it's extremely doubtful they'd resemble anything like each other by the time they were reunited by air travel.
Then maybe "Common", introduced from over the mountains by the newly arrived travellers, is easy to pick up - so maybe it quickly gained popularity even internally to Doma, as a way of communicating between isolated communities with incomprehensible dialects - so in modern day, lots of Domans speak it (and thus find it easy to acclimatise to Eorzea, which only has a slight difference in accent from the Common they learned at home). But I think it pushes the bounds of belief to suggest that everyone in Doma would be perfectly happy to abandon their old language (thus rendering it dead) in favour of this one, in the span of a generation. And we already know Raen live in Doma for the most part... so...
IDK. Maybe there'd be teenagers who grew up speaking Common only, but I reaaaally don't think it'd be the norm.
Sticking with my "Common is a trade language; Doman still exists as a local language" theory.
Edited to elaborate: Like 20 years is still a decently long time to integrate a new language into society if it's useful enough, but I also don't think it's enough time for the old language to totally die out. Othard's cultures were isolated for centuries; they will have developed language families, dialects, and all the related oddities independent of anything an Eorzean would be familiar with. Even if the two Hyuran populations either side of the mountain-range began with the same language, it's extremely doubtful they'd resemble anything like each other by the time they were reunited by air travel.
Then maybe "Common", introduced from over the mountains by the newly arrived travellers, is easy to pick up - so maybe it quickly gained popularity even internally to Doma, as a way of communicating between isolated communities with incomprehensible dialects - so in modern day, lots of Domans speak it (and thus find it easy to acclimatise to Eorzea, which only has a slight difference in accent from the Common they learned at home). But I think it pushes the bounds of belief to suggest that everyone in Doma would be perfectly happy to abandon their old language (thus rendering it dead) in favour of this one, in the span of a generation. And we already know Raen live in Doma for the most part... so...
IDK. Maybe there'd be teenagers who grew up speaking Common only, but I reaaaally don't think it'd be the norm.