Why do male last names in Icelandic end with -son instead of -sonur?

Svar

In Old Icelandic, when the word sonr formed the second part of a compound, i.e. Magnús-son, Sigurðs-son, the final -r (-ur) was dropped in nominative singular, and the same morphology is used in Modern Icelandic. E.g.:

• Nom. Magnús Sigurðsson (son(u)r)
• Acc. Magnús Sigurðson (son)
• Dat. Magnúsi Sigurðsyni (syni)
• Gen.Magnúsar Sigurðssonar (sonar)

In the word dóttir on the other hand, no change of this sort occurred. In Old Icelandic the ending was -er (-ir) in nominative singular and -or (-ur) for all other cases. Again, the morphology remains unchanged in Modern Icelandic.

• Nom. Guðrún Sigurðardóttir (dóttir)
• Acc. Guðrúnu Sigurðardóttur (dóttur)
• Dat. Guðrúnu Sigurðardóttur (dóttur)
• Gen. Guðrúnar Sigurðardóttur (dóttur)

Further answers in English:

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• How did the Icelandic language start? by Guðrún Kvaran
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• How many words are there in Icelandic? by Guðrún Kvaran
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The original question was:

Why is it that male last names in Icelandic are in accusative -son instead of nominative -sonur, even when referred to in nominative, whereas female last names are referred to in nominative case -dóttir and not -dóttur?