It wouldn't be strange or anything for Ahnasha to have no surname, if I'm understanding properly. Khajiit don't have family names. Though, the same is also true of the Bosmer, so I don't know what she could be said to be descended from.
It makes sense in the ceremony, though unfortunately, Ahnasha doesn't actually have any family that would have a surname. I think saying something along the lines of "Ahnasha, daughter of Gwindir" would fill the same function. At this point, she wouldn't have a problem naming her family members. Especially since it wouldn't actually be easy at all to track down someone with just a first name, across possibly all of Tamriel.
That makes sense, I guess. I changed the explanation, but I'll edit it in like that instead.
Edit: Done. I'll ask you if there are any other details like that. I'm honestly making up this ceremony without too much thought ahead. I don't think there are any sources on Dunmer marriage in the lore.
For the sake of brevity, you can play out the priest reciting the words for Ahnasha. I don't think trading tiny posts like that has much of a point for this.
Just spent several hours doing a large post for another RP, wasted a lot of time failing to look for soundtracks for it because I'm something of a fool tonight. It's 1:30 AM. Things are on tomorrow during the day...
I'm afraid my next post won't be up until late tomorrow.
This wedding's been working out pretty well though.