Þórarna is a Old Norse compound name with the first element Þór-, from the name of the god Þórr ‘Thor’ (very common in both male and female names), combined with -arna, the feminine form of -arinn, either from arinn ‘hearth’ or more probably the postulated element *arin related to ǫrn ‘eagle’. 

A couple of instances of Þórarna are recorded in Norway with one of the earliest being from the ninth century. The name is frequent in Iceland evidenced by the multiple mentions in Landnámabók ‘The Book of Settlements’, a quasi-historical text which recounts the settlement of Iceland. Þórarna is not attested in Denmark or Sweden. There is a form of the name found in the Yorkshire Domesday, but it may alternatively represent the male name Þórormr.