Their name for themselves is variously given as Nod-doh-wa-ge:o:no (yes, the colons represent a phoneme, but I don't know what it is) or Onondowahgah both of which mean People of the Great Hill. AHD gives the origin of the name Seneca, referring to the Indians, as From Dutch Sennecaas, probably of Mahican origin. M-W adds that Sennecaas means the Iroquois living west of the Mohawks. I wouldn't be surprised if there were some connection with the Roman of the same name, if only in affecting the spelling. I included the two only to indicate that, in my opinion, there need be no connection between two entities for them to be called namesakes.

Nation originally referred to a people and not to a political organization. It derives from the Latin word meaning to be born.