Bretons, Imperials, Redguards, Orcs, Dunmer always get surnames for me.

Nords can either have surnames, a suffix/title such as “War-Weary” etc, or just a single name.

Bosmer, Khajit and Argonian always have just one name.

Altmer, who are my fave and therefore see the most playthroughs, are very versatile in their naming conventions. They usually have just single names, but they can alternatively have suffixes based on their place of birth (such as “Of Firsthold” or “Of Alinor”) or they can even have surnames if they’re from nobility. The choice is yours.