The strategic (or perhaps Operational, in German staff parlance) importance of Stalingrad is that it is a crossing on the Volga river and at the time an important railroad junction. Check out this [map] (http://en.wikipedia.org/wiki/Battle_of_Stalingrad#mediaviewer/File:German_Summer_Offensive,_7_May-23_July_1942.PNG)

If the Germans took Stalingrad the Soviets would lose communications with the entire Caucus region. Additionally water traffic on the Volga river would be cut. Instead of the Germans being caught in an enormous salient (bulge) the Russian forces south of the city would be cut off.

Futhermore, with a bridgehead on the Volga, the Germans might have been able to push even farther east.

The political factors because of the city's new name were secondary.