I mainly agree with John Hostage--it's debatable, and there should be some guidance. Just to make the counter argument:
Use of a controlled form of name for a birthplace indicates an intention to provide uniform access. Birthplace is not a subject heading, but practice now is to regard many attributes as access points with vocabularies that support uniform retrieval. If the birthplace is simply an attribute derived from sources, one could (and one can) record any found form with the appropriate field/subfield designation. But if the intent is to support uniform retrieval, using a single heading for a city where persons were born does that better. The instruction about not using Danzig (Germany) for subject headings is implicitly about using Danzig (Germany) only for name entries. The birthplace attribute is not a name entry, either. Hence the need for guidance.
Given that in this case the city not only changed its name but its nationality, another option would be:
370 $a Gdansk (Poland) $2 naf
370 $a Germany $2 naf