Lesbian (gay women) vs. Lesbian (people of Lesbos)

Saw this in the news this morning:

People of Lesbos take gay group to court over term 'Lesbian'

I don't know how they expect to change widespread global use of the word "Lesbian." However, I see their point. It's probably easier to come up with another good term for gay women (bland as "gay women" is, it would probably suffice), than for the people of Lesbos (who have been properly called Lesbians for millennia) to find another name.

So if the word "Lesbian" becomes restricted to the geographic designator in Greece, would the rest of the world follow? Not immediately, but over decades, I suppose it's possible that global use of the word could shift. It probably would anyway, with or without this lawsuit, as it is the nature of language to change.