Clearly he is a Danish king. Does the "Half-Dane" indicate that he is half Swedish?
From the Wikipedia article, summarizing from the Ynglinga Saga:
Halfdan attacked King Aun of Sweden and drove him into exile into Götaland. Halfdan then ruled Sweden for twenty years until he died in Uppsala of sickness and was buried in a mound.
It seems like Sweden would be the most obvious explanation for Half-Dane's "other half."