While Germany does have some variety in its dialects, that variety has precious little to do with the recent political division of the state. Rather, the country is roughly divided into horizontal thirds, representing Low German, Middle German, and High German, respectively. You can make the case that these dialects are further sub-divided (usually into eastern and western halves).

While the division may have had some impact on local dialects, the cultural differences caused by the division are much more readily apparent. You can read a brief summary article of that here (in German).

As a non-historian german: No. There are the usual dialects but those are like everywhere dependent on the location in general and not caused by the political division. We sometimes speak of an "Ossie-Akzent" ("Ossie" short for someone from the former DDR), but this dialect was the same before and after the DDR.

There's been a few similar questions asked here in the past that you might be interested in:

• East and West Germany were separate for a few decades. This means there was limited language contact. Did this have any effect on language variation (as compared to how American and British English evolved)? posted on 27/09/15

• Did the German language as spoken in West Germany and in East Germany diverge? posted on 27/11/13

Since both of those questions are over 6 months old, If any of the answerer's comment in those threads interest you, feel free to tag their username with your follow-up question in this thread .

Hopefully this helps :)