Most Bosmer do not have family names, but there are a few exceptions.
From UESP's lore article on Bosmer Names. It doesn't cite a reason, but they seem to appear almost exclusively in Daggerfall and Arena. I could be wrong about that though. I'm not at all familiar with those titles, but someone in the Lore group might be able to better answer your question. Try this thread.
I know SpottedFawn is around here somewhere, she's kind of the Bosmer master. I know she worked on a huge project about the Bosmer with Karver and Thorien, so they may be better able to give you a satisfactory answer.
Bosmer definitely have surnames, but I think there´s a reason why Niruin doesn´t use it.
To be more specific, Bosmer are kind of a...tribal, but it is rather complicated. Because there are Clans in Bosmeri culture too. For Orcs, Clan and Tribe means the same thing, because tribe is one family.
Bosmeri tribes can consist of more than one clan, or just one clan. So clan is basicaly your family, the name of your clan is your surname. I mean, family for Bosmer are the closest ones. Clan are cousins, uncles and such.
So I imagine that Bosmer don´t need to use the names of their clans in foreign countries.
It´s actually funny when you think about it, because Nords have clans too, right? Stone-Fist, Shatter-Shield and so on.
Thanks for the response! I was kind of thinking along the same lines. I ended up creating a surname of Nightbrook for my character Vander who is the younger brother of Niruin in my story. If for some reason I found out later that this does not work or that Niruin, in fact, has a surname then I will make them half-brothers!
Happy to help. And I wouldn´t really worry about finding out Niruin´s surname. I was looking for it by any means neccessary when I saw this and haven´t found a single mention. If Bethesda wanted Mer NPCs to have surnames in Skyrim, they would do it. So Nightbrook sounds fine by me.
Also, maybe next time you have questions like this, I would head to Lore, to Ask your lore questions here, that´s where we usually discuss stuff like this. Me, Phil and others check it quite often.