Names

[BørkBørk]

I was looking at icelandic names on the net and noticed that a lot of them end in -ur (e.g. Leifur). As far as I know, the -ur is a grammatical ending, and I was wondering if you use it when calling someone's name (i. e. do you shout "Leif!" or do you shout "Leifur!").

Also, if someone pointed to a ring and asked "what is that?", would you answer "hring" or "hringur".

[Noreviking]

Names in Icelandic are inflected like other nouns. Hence you'll have to deal with the nominative, accusative, dative and genitive case when talking about someone.
If I'm talking to or calling my Icelandic friend, I usually use the nominative form of the name (which can end in -ur or something else. This depends on the gender of the noun). If you're talking about a person who's not the subject in the sentence, or there are certain prepositions used before the name, you usually have to use one of the other cases.

[BørkBørk]

When you are calling someone by their name, you're not forming a sentence; there is no subject or object or anything. I was wondering whether Icelandic used the stem (e.g. "Leif") or the nominative case (e.g. "Leifur") for this.

Also, do names have genders of their own or do they take the genders of their bearers?

[Halfdan]

Well, considering that Icelandic no longer employs the vocative case, it is likely that the nominative of the names. Except in a few cases like Jesus:

Jesús elskar þig. (nomative) Jesus loves you.
Ó Jesú, frelsari okkar. (vocative) O Jesus, our saviour.
Source

But I don't believe that applies to modern names.