I understand that the issue in Iceland is that it is an inflected language, and names, like other words, change form depending on the grammatical function of the word in any sentence. The limit on what names you can choose is to ensure that children's names can 'fit' with Icelandic word forms.
I don't think names should be limited to approved lists, as that can discriminate against families with different ethnic identities and naming traditions. However, I do sometimes think it would have benefitted some families if the registrar had had a quiet word ...
In the interests of transparency, my own children have names that have attracted a fair number of negative comments over the years. You can tell when someone hates the name because they say, "That's very... (awkward pause) unusual." They are both real names with long (in one case, 700 years long) histories but unusual enough for people to think I made one up!