Okay then, where'd Rome come up with it? Oh, "the land of the Germani," but scholars are divided on the origin of Germani. Possibly from Celt gair, "neighbor." Or maybe from a few other sources.

The word germ also comes from Latin, "sprout" but I'm not seeing anything like "people who sprout" or "from the land of sprouting seeds" or anything else to connect them at all. It's more like ger+man.