According to Vasmer and Vinogradov, варяг is loaned from Old Norse *varingr, "a trusted one", remotely related to Russian вера.

At the time, Slavic has nasalized vowels ѧ and ѫ (preserved in modern Polish as ę and ą), the former sounding similar enough to -in- to substitute it in loanwords.

Later Old Slavic nasalized vowels turned into a and у in Russian so *варѧгъ became modern варяг.

There are several other Germanic loanwords following the same model: князь < *кънѧзь < *kuningaz (PG), витязь < *витѧзь < *vikingr (ON), чадо < *чѧдо < *kind (disputed) etc.

On the other hand, Finnish, which had also loaned words kuningas and ruhtinas from Proto-Germanic, preserved the combination -in-.

This fact, as well as the fact that the loss of nasalized vowels was a common Slavic process not limited to areas populated by Uralic-speaking people, argues against Uralic influence on the loss of the nasalized vowels and hence я in Russian варяг.

According to Vasmer and Vinogradov, варяг is loaned from Old Norse *varingr, "a trusted one", remotely related to Russian вера.

At the time, Slavic had nasalized vowels ѧ and ѫ (preserved in modern Polish as ę and ą), the former sounding similar enough to -in- to substitute it in loanwords.

Later Old Slavic nasalized vowels turned into a and у in Russian so *варѧгъ became modern варяг.

There are several other Germanic loanwords following the same model: князь < *кънѧзь < *kuningaz (PG), витязь < *витѧзь < *vikingr (ON), чадо < *чѧдо < *kind (disputed) etc.

On the other hand, Finnish, which had also loaned words kuningas and ruhtinas from Proto-Germanic, preserved the combination -in-.

This fact, as well as the fact that the loss of nasalized vowels was a common Slavic process not limited to areas populated by Uralic-speaking people, argues against Uralic influence on the loss of the nasalized vowels and hence я in Russian варяг.