The word "Germani" is first popularized by Caesar, he used it to group a large population under one label and he built a narrative with it. There is a debate among scholars to know if Caesar was really the original source, maybe Posidonius of Apameia was the actual original transmitter of the word. But there is no consensus. Furthermore, there is a plausible hypothesis where Posidonius transmitted the named "Germani" to specifically speak about a tribe, not a large group. Tacitus mentioned that the name was originally applied to the Tungri only, then it has been generalized to others. Maybe Tacitus was relying on Posidonius because Caesar doesn't mention the Tungri. Caesar mentions the Aduatuci, the Condrusi, the Eburones, the Caeraesi and the Paemani as being commonly named Germans. Which is interesting because the Tungri could be another name of the Aduatuci. Finally there is something interesting in relation to the Cimbri here: The Aduatuci are a remnant of the Cimbri and Teutones who tried to invade the Belgians and failed. This is explained by Caesar. So the descendants of the Cimbri and Teutones could have been called Germans a few decades after their wandering.
Thus, the Romans did call a large population Germans. German is not a label the tribes used to call themselves, but so do is the name Gaul. The concern with the name Germans and its correspondence with present-day Germans dates back to the Second World War and the Nazis' use of the Germanic theme as an ideological justification. But at no point is anyone going to make the same criticism of the use of the name Greek for the ancient populations of Greece when the Greeks of today bear the same name. The same goes for the Egyptians, the Chinese, the Belgians etc. I don't see why today's Germans should have exclusive use of this name. What's more, the problem only exists with English, and the world does not revolve around Anglo-Saxon countries alone. ‘Deutsch’ in German. ‘Allemands’ in French. ‘Tedeschi’ in Italian. ‘Alemán’ in Spanish.
For me, the only problem with the Cimbri is that they come into conflict with a future faction of the Germans and that they're a single, relatively unknown people. The concept seems interesting, although I haven't tried the faction out yet. If we rename the Cimbri as Germans, it is fine for me. Although it is a bit sad to reduce the Germans to a single tribe.