To quote myself from a previous time this question popped up:

It's purely coincidental. The English name for the nation is derived from "Osininka," one of the major Onöndowága towns. Onöndowága is the proper name of the Seneca, but even other Iroquoian people tended to call them "Osininka" after the town to distinguish them from the Onöñda’gega’ - the Onondaga - whose principle town had the same name as the nation.

English-speaking colonists had a tendency to drop initial vowel sounds from Native names, which is how Ojibwe become Chippewa in English. The Iroquoian nasalized vowels, as in Osininka, are often hard for English-speakers as well, so it loses the nasalization. So, all things considered, Osininka morphs into Seneca in English.