I associate this name with Game of Thrones now, because the character of
Asha Greyjoy was so impactful. I imagine someone strong-willed, possibly a bit bratty. There is something a bit empty about this name for me.
I say it "ASH-ah". I've never met one in real life.
I'd say it's just as legitimate to say it means "ash tree with a feminine suffix" as well as "ash, with a feminine suffix" (which is what I think of - ashes) because that just makes sense in English.