So the accusation "this name is made-up" would be rather pointless there. The parents (or the paternal grandfather) make up the names. There used to be a "generation part", common for all siblings (or all siblings of the same sex) and an individula part. Examples: Ai-ling, Chong-ling and Mei-ling for three sisters.
In practise, parents have limited imagination so therefore there are many children with the same names. Also, while some names sound good for both sexes, some are definitely for girls (names with flowers for instance).
I have no proof but I am certain that in Iceland it depends on a). Many Icelandic names are old names, used before Christianity was introduced. So c) does not apply. And I don't see what European has to do with, since other European countries don't have the same rules. In Sweden, for instance, immigrants keep their names, however strange they may sound to Swedish ears.