There is a convincing theory that the surname Farthing is derived from the name of a viking warrior named Farthegn meaning travelled thegn, where thegn means warrior. The name may be spelt other ways, e.g. Faerthegn etc, and may have also become varied as Firkin. There is a legendary king of that name. The name of the Northamptonshire village of Farthingstone is believed to have come from this source.
There is a detailed examination of this theory at a site on the "Genring" Webring which at the time of writing this, 2010, is at:
There is also a page at the site:
but the relevant page is hard to find.
Try searching Wikipedia for 'farthegn'