true-ish. I'm not aware of any tribes that would give name to Deutsch and Nemti. Rather, Deutsch is the generic self-description for all tribes, and Nemti was a generic description of all tribes by slavic people (ie Niemy in polish meaining "without the ability to speak")
I thought:
Deutsch: https://en.m.wikipedia.org/wiki/Teutons
Nemți: https://en.m.wikipedia.org/wiki/Nemetes
But at least Deutsch does indeed appear to have other origins according to: https://en.m.wiktionary.org/wiki/deutsch