"a friend of Nina's" is an example of double possessive. It is used to avoid ambiguity. In the case of "a friend of (name)" it is not necessary, but with other phrases, it is. a picture of Nina = a photograph that Nina is in a picture of Nina's = a photograph that is in the possession of Nina a student of Einstein = somebody who studies Einstein (his life and work) a student of Einstein's = somebody who is in Einstein's class Because of these other cases, we use it even where it is not necessary. a friend of Nina = one of Nina's friends a friend of Nina's = one of Nina's friends In this case, there is no ambiguity and they mean the same. With the name of the restaurant, there is also no ambiguity.

I have actually never heard the first one. It is correct to say 'a friend of Nina' which means Nina's friend and 'the name of the restaurant' which means the restaurant's name. Unless you want to say that Nina has dog and her dog has a friend, you can say something like: A friend of Nina's dog. Hope this helps! :)