Woden has in the region of 200 by-names in the Eddas, one of which is Vidrir, which appears on face value to be uncannily similar to Vidar, His son. These are the references to Vidrir in the Eddas:
"Be silent, Frigg, you're Fiorgyn's daughter and you've always been mad for men: Ve and Vili, Vidrir's wife, both were taken into your embrace." (Lokasenna 26, Elder/Poetic Edda, Larrington translation).
"Be thou silent, Frigg! Thou art Fiorgyn's daughter, and ever hast been fond of men, since Ve and Vili, it is said, thou, Vidrir's wife, didst both to thy bosom take." (Thorpe translation).
"The warriors went to the trysting place of swords, which they had appointed at Logafioll. Broken was Frodi's peace between the foes: Vidrir's hounds went about the isle slaughter-greedy." (The First Lay of Helgi Hundingsbani 13, Thorpe translation)*
"He is called All-father in our language, but in Old Asgard he had twelve names. One is All-father,.........the eleventh Vidrir,......." (Gylfaginning 3, Younger/Prose Edda, Faulkes translation)
"The poet Bragi said this: Vidrir's [Odin's] heir's [Thor's] line lay by no means slack on Eynaefir's ski [boat] when Iormungand uncoiled on the sand." (Gylfaginning 4)
"And on the island, instead of the Vidrir [warrior] of the mail-coat's troll-wife [axe], the victory-preventing witch of a woman had her way." (Skaldskaparmal 50, Younger/Prose Edda, Faulke's translation)
"I used to win land for myself like earls of yore with staves of the rod of Vidrir's [Odin's] weather. I had a reputation for this. (Skaldskaparmal 50)
"I go west over the depth, and I carry Vidrir's [Odin's] thought-strand-[breast-] mere [mead of poetry]; this is my way." (Skaldskaparmal 61)
It is interesting that Vidrir alliterates with Vili and Ve which may be an indication of its antiquity. Rudolf Simek in his Dictionary of Northern Mythology interprets the name to mean 'weather god' and yet he goes on to state that "Odin is naturally not the actual weather god of Nordic mythology; he influences it, however, by magic." However he fails to take into account that amongst the continental Germanic peoples Woden had a greater association with weather, especially stormy weather than the later Scandinavian Odin. See my article http://aryan-myth-and-metahistory.blogspot.co.uk/2012/10/woden-and-vata-vayu-comparison.html
Another interesting by-name for Woden is Vidurr. Simek is unsure as to its interpretation but speculates that it may mean something like 'killer'. It could also indicate that Vidurr (Woden) is the eponymous ancestor of the Wederas or Weder-Geatas from Gautland. (Simek). Grimnismal 49, Elder/Poetic Edda refers to "Vidur in battle." Vidur is also listed as one of Woden's by-names in Gylfaginning 20. Like the name Vidrir, Vidurr can also mean 'poetry', one of the specialities of the All-Father:
"No need for men to nurse fear about my poetry. In Vidur's [Odin's] booty I use no spite. We know how to order praise-works." (Skaldskaparmal 3).
"I shall continue to compose more praise about the renowned son of Sigrod; I shall pay him the stipend [poetry] of the gods' atoner [Odin]. Thor sits in his chariot." (Skaldskaparmal 54)
There is certainly an overlap of meaning between Vidrir and Vidurr (battle and poetry) and it is tempting to see a relationship between these two by-names of Woden and that of his son Vidar (Widar). V and W are interchangeable in Germanic languages and we see the following coincidences:
Woden (Voden/Vidrir/Vidurr) + Wili (Vili) + We (Ve) = first generation of Aesir and
Widar (Vidar) and Wali (Vali) = second generation of Aesir.
The All-Father truly lives on in His son. This is certainly a theme that requires further development.