Female surnames are most often in the Katharevousa genitive case of a male name.
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Linguistically, the thesis of the genitive case dying out can easily be refuted.
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You also swapped the dative, instrumental and genitive forms in the 3rd person.
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The genitive plural, however is hjartna showing a-breaking instead of u-breaking.
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Genitive noun forms are essentially archaic and not part of common usage anymore.
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The order of the genitive and the governed word is always the same as in English.
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Tone is not written, except indirectly in genitive phrases, which are hyphenated.
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For such nouns, the genitive singular must be learned to see if the E is dropped.
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Tag-iya or genitive markers mark the owner of the thing or the doer of an action.
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More examples
Possessive: serving to express or indicate possession; "possessive pronouns"; "the genitive endings"
The case expressing ownership
In grammar, the genitive case (abbreviated ; also called the possessive case or second case) is the case that marks a noun as modifying another noun. ...
(genitively) In a genitive way
A declension in any synthetic (i.e. heavily inflected) language that indicates possession. In many Old English singular nouns, an -es declension attached to the end of that noun would indicate the genitive case. ...
One of the six cases in Latin. In addition to a few specialized uses which have to be studied separately, the genitive case very often shows possession, and therefore can be translated with our preposition of or the ending -'s.
A grammatical case in Greek. In English, if we wish to denote possession we can either say 'The book of the girl' or 'The girl's book'. The second phrase demonstrates how, in English, a noun (girl) can be inflected to indicate possession. ...
Noun case expressing origin or possession, e.g. "Rome's citizens, John's book".