IIRC the reason that the family got the name "Germanic" is basically that it was some Germans that came up with the idea. I'm having trouble sourcing this though.
Last I heard was that the German tribe the language group was named after weren't even germanic soeakers. Like the fact that the Franks were a germanic speaking tribe who abandoned their language for the local dialect of latin which become French.
The German word for the ancient Germanics isn’t the same as their word for present-day Germans (Germanen vs. Deutsche).
The romans called the area Germania after the germani that lived there. Germani is believed to be a celtic word though. So it's possible that the original Germani were actual celtic speakers. Which is another branch of old indo-european.