Icelandic Female Surnames and Marriage

[Resist]

Icelandic surnames are patronymic or matronymic, i.e. the son and daughter carry their parents' name. Jon Eriksson and Eva Eriksdottir for example. I have the following question: what happens when Eva Eriksdottir gets married to someone named Jonsson or Gunarsson? Does she retain her surname, or does she become Eva Jonsson or Eva Gunarsson?

[thoughtcrime]

She'd retain her surname. Icelandic surnames don't function as family names, like central european ones. Therefore, if Eva Eriksþottir gives birth to a child, it will have another name than her! As far as I know, the icelandic surnames are more like "titles", you don't even adress someone as "Mrs. Eriksþottir", not even on a formal level, but as "Eva" or "Eva Eriksþottir".

Correct me if I'm wrong, I'm not icelandic myself, that's just what they told me at university (I studied nordic philology for 2 semestres.)

[Blod og Jord]

totenlicht is right,
women in Iceland don't change surname after marriage.
There isn't a suffix which is used for wife,
like for son and daughter.
So a woman remains her father's daughter even after marriage,
forever.
References by first name are very common.
You can even address public figures and politicians,
even the president,
by their first names.