Thank you both for the fast replies 
I will take a look at mkgmap and try to understand how to use it! Maybe I should explain my Idea a little bit more detailed:
I’m working on an autocomplete field which suggest streets + cities in a search form. E.g. you type “Ma” and it should suggest
“Main Street, Wiesbaden”, “Main Street, Hamburg”, “Max Street, Berlin”, “Monster Street, Heidelberg”.
So, it is not that important that the data is 100% correct as the user still can insert the street manually.
I know this can be done with OSM, because some other platforms like pizza.de (I think I saw OSM in the imprint) and http://www.zeit.de/interactive/strassennamen/ use OSM Data, so it should be possible to connect streets to cities.
I will take a look at mkgmap and tell you about my results!