The Dictionary of British Place Names explains the origins of the names of towns in the British Isles. Is there a comparable dictionary for place-names in Germany (or in the entire German-speaking world)?
There is no “global” dictionary for the German-speaking area. Instead, there are lots of regional projects that often cover individual districts (Landkreis). A common term for such a dictionary is Ortsnamenbuch.
As an example, there is the Westfälisches Ortsnamenbuch, planned to comprise 19 volumes, of which 8 volumes have been published as of March 2016. Unfortunately, I am not aware of a complete list of similar dictionary projects; only a few of them are listed in the Wikipedia article Ortsnamenbuch.