Every Monday we will post an entry that hasn’t yet been published with a view towards harnessing the collective onomastic power of the internet. If you have any thoughts about the name’s origin, other variants it might be related to, other examples of its use, etc., please share them in the comments! If you wish to browse other Mystery Monday names, there is an index.
Today’s name is an Italian name from the late 13th/early 14th C. It has a V! It has a Y! Neither of these letters are especially common in Romance languages, and the combination of the two results in an unusual name. Have you seen any examples of it? Do you have thoughts on its origins?
Dictionary of Medieval Names from European Sources 
So far I have found Vayra as a place-name and river-name and as an apparently locative byname in south central France, though I’d have to do some digging again to recover the references. Closer to the instance in question, I’ve also found it as a surname in Piemonte:
Ferdinando Gabotto, Documenti inediti sulla storia del Piemonte al tempo degli ultimi Principi de Acaia (1383-1418) in Miscellanea di storia italiana, third series, vol. 3, Torino, 1896, p.232, in a document of 1409: Libravit domino Vayra de Vigono, magistro grosse bombarde domini Principis, pro expensis suis et duorum famulorum suorum et unius ternerij, … . On p. 257, from 1412: … magistros Johaninum de Mondino et Oddonellum Vayram … . The index identifies these as the same person, Oddonello Vayra.
I’m inclined to suspect that your example is also a surname, if only because I’ve found no clear example of Vayra or similar as a forename.
The only possible etymology that comes to mind requires either that the name have originated in France or that in northern Italy it is the result of similar developments in some Gallo-Italian dialect, so it’s at best highly speculative. Vayra is a reasonable spelling of a Gallo-Romance or Old French reflex of Latin varia ‘variegated; changing, inconstant’; as a river-name it may be from varia aqua. Similarly, the nomen Varius with the locative suffix -acum (of Gaulish origin) is the source of the place-name Vayrac.