The name "Cymru" and "Cumbria" in Brythonic (mind you: we are talking about Modern/Medieval Celtic languages here, not Classical) is generally thought to be a contraction of what would have been "Combrogi" in ancient Brythonic (literally, "together-homelanders", perhaps better "compatriots"). So, in the 2nd century BC, what we would expect is really "Combrogi", not "Cimbri".
And well, I did not say that there was an easy solution to the problem. I just suggested a possibly Germanic etymology for "Cimbri". In fact, a modern cognate for "Cimbri" may exist in the region of Himmerland in Denmark.
As for the overtly Celtic personal names of their leaders, this poses a significant problem not only with the Cimbri but with other tribes that are usually considered Germanic: of the Suebi (Ariovistus), as well as for instance of the Markomanni (Maroboduus, Ballomarus, Ariogaesus). What is the solution here? I would argue the solution is that the Germanic tribes in this stage were heavily culturally dominated by the Gauls, and that it was common for the upper echelons of Germanic society to speak Gaulish and have Celtic personal names. Given how the Suebi are apparently invited with ease to assist the Arverni during the Gallic War, you get the impression that the language barrier was really non-existent.
Is there any other evidence this really was the case? As a matter of fact, there is: the Germanic languages do have a sizable number of Celtic loanwords (notably the word for "iron" and the word for "foreigner"), basically all which date to before the First Germanic Sound Shift. Archaeologically, we could indeed see this in the shape of the Jastorf Culture.
Another evidence comes from Celtic place names: we do see Celtic name evidence extend deep into Celtic Europe, at the Rhine delta, along the Rhine, from the Danube northwards as far north as about the Main river, the Erzgebirge and the source of the Oder river. We get a clear picture that these regions must have been linguistically Celtic until circa the 2nd-1st century BC, and this also roughly corresponds also with the maximum extend of Hallstatt and La-Tene in these areas, however there is an "indent" that roughly corresponds to northern modern-day Hesse (as well as adjacent areas on the right-bank of the Rhine and north-bank of the Main) where no Celtic place names can be found, yet archaeological evidence for Celtic culture is ripe. The only sensible solution I see is that these areas in the north were not ethnic Celtic, but only culturally.