The short answer is: other than in the USA, where it is common to add to names of towns and other inhabited places an abbreviation to indicate the federal state, e.g.
this is not common in German speaking countries.
There are, though, traditional additions to names such as Frankfurt that exist twice or more. These additions, however, do not follow a general rule. They are specific in kind and spelling for each individual place. Therefore you have
Frankfurt (Main) [also: Frankfurt am Main]
Frankfurt (Oder) [interestingly never heard: Frankfurt an der Oder]
Neustadt an der Weinstraße
Neustadt am Rübenberge
Biberach an der Riß [also: Biberach/Riß]
Some of these additions have remained pure disambiguations; other have become practically unseparable parts of the toponyms e.g.
Zell am See
which nobody would think of as just "Zell" leaving out the lake, whereas one usually would go nach Frankfurt, and only add the river when there can be doubts.
Some municipalities have incorporated landscape features into their official names in order to use it for marketing (making clear that this particular place is situated in a region known for its beauty), e.g.
Leutkirch im Allgäu
where "im Allgäu" is not really necessary as there is no other Leutkirch anywhere, but people want to mention the Allgäu region because it is famous for being lovely (green grass and forests, brown cows, undulating hills), and part of the economy relies on tourism.
(Anekdote: I once spent a weekend to visit the aforementioned Neustadt am Rübenberge because I imagined the town being situated at the foot of some lovely hill in the otherwise flat and boring Lower Saxonian landscape. Boy was I disappointed. No distinguishable Rübenberg there far and wide. Obviously the municipal marketing had gone too far here.)
Otherwise, it is not common to add the German federal province to a place's name. German federal provinces are also not mentioned in postal addresses. Exception: with the emergence of US-based online traders, sometimes we are faced now with customer profile forms that necessarily require a "state" to be entered, clearly just because the form was desigend like that for use in the US market. For Germans (and I suppose also for Austrians and Swiss etc.) this is rather a nuisance.