Why do we say "German" when the real word is "Deutsche"?!
To the French, we are "les Allemands" (actually one of many "german-speaking" tribes whose home was close to the French border).
To the English, we are "the Germans" as a group of tribes was actually called by the Romans (The Romans being in England AND Southern Germany at the same time (100-300 AD methinks) the name may come from that period.
The word "Deutsch" comes from an 1500 year old word "tiutisc" meaning "the people" (as is the case in a large number of languages) and modern Italian has taken "tedesco" (=a german) from that.
Linguistics are always a tricky business.