Why is there a V in "Peruvian"?
Solution 1:
Wikipedia gives the etymology as Piruw [pɪɾʊw], from Quechua, the Inka language.
That [w] at the end would become a /v/ in Spanish when adding a suffix to produce Peruviano.
English demonyms have lots of odd features, and this isn't even English demonymy.
I remember when I was in grad school we used to try to figure out what kind of process
could possibly produce Glaswegian from Glasgow, and Norwegian from Norway.