Uwe....
You are absolutely correct! Hilda (yes, originally Hildagarde) is my great grandmother with "Willy" being both August's son and her father. She was nearly 2 years old at the time this letter would have been written and Geth (which must be a pet name variation for Elizabeth) was her aunt and also her godmother. They remained VERY close their whole lives. Okay...so this makes much more sense. This is a very endearing letter which touches my heart and gives me such a glimpse into a bit of the family. It is such a treasure to have been kept in the family and now I see why my great grandmother Hilda kept it for her whole life. Without even knowing family names, you got it right!