Until 2002, nearly every ICE, EC and IC train in Germany beared a name. Now, there are only a few trains with a name, like EC "Vindobona" or EC "Wawel" to Poland. The DB doesn't baptize its trains any longer, but it baptizes its ICE units with names of cities, as Lufthansa also does.

Yes, that's true. Only very traditional and particular trains which have existed for more than a couple of years still have their names. Another famous example of this is the IC 2082/2083 "Königssee", which travels from Hamburg to Berchtesgaden in the German Alps (it's the only main-line train which reaches this area). Here is a very nice picture report of this route.

Regards,
Claus_NN