$record->getRelatedSet('Related set name with umlaut') (e.g. $record->getRelatedSet('CT_Services_Pläne_Objekte2'))
doesn't so and does not recognize the name of the related set.
The corresponding XML fmresultset query returns the related set name correctly with umlaut and in UTF-8 Unicode (as it always did since FMSA 7), hence, it must be a problem of the PHP API implementation:
I had to rename the TO from CT_Services_Pläne_Objekte2 to CT_Services_Plaene_Objekte2 .
I'm using FMSA 11, the corresponding PHP API, and PHP 5.3.8.
Lesson learnt: Don't use umlauts in TO (and also field) names, even if the transliteration will hurt your eyes. One never knows whether one will have to use other methods (SQL, ODBC, JDBC, PHP etc.) for accessing the DB.