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I found no statement as to the actual etymology of the name. It is easy to establish that in modern Iceland, the connection to Thor is made, and this interpretation probably dates to before the modern custom. It is also evident that the meaning :"frost" is derived from the month name, and the month name is derived from the Thorrablot, and Thorrablot from the character Thorri. But I find no positive statement as to just how the original name could have been derived. I found old literature listing it as one of the "many Norwegian names derived from Thor", but no positive claim that the name is in fact originally a diminutive of the name Thor itself. More recent literature mostly ignores the character, or just mentions him briefly as a frost-giant or similar.
My personal opinion is that we have an artificially unified picture of Norse polytheism because most of our material was redacted by Snorri, and that Thorri is in fact a reflex of a non-Eddaic tradition of Thor. This is would not be surprising to anyone familiar with Greek polytheism, where the better attestation of regional traditions shows that theonyms take all sorts of variant forms in regional traditions. But this is speculation. The fact is, of course, that Thorri in the medieval sagas appears as an independent character. It appears that the saga tradition even states that Thorri's sister was abducted by a giant who was a grandson of Thor, which makes it clear that in this saga at least Thorri cannot be Thor.
Vulpius (1826)  distinguishes a Norwegian Thor (Asa-Thor) from a Finnic Thor (Thorri). Nilsson (1868) also says that Thorri is "evidently" Thor. I think Barth (1846) was on the right track when he said that when Thor joined the "church of Odin" he was adopted as Odin's son and given the title Asa-Thor. As Asa-Thor he apparently turned against his own kin, defeating the Jotuns and destroying the altars of Fornjotr. But this doesn not necessarily reflect the competition of a "foreign" Aesir cult with an "indigenous" Jotun cult, it could just as well be a reflex of a Germanic "Theogony" or "Kingship in Heaven" where one generation of gods defeats the preceding one, as part of Indo-European myth from day one. --dab(𒁳) 17:47, 17 November 2010 (UTC)