The mother’s name is Barbara Blocksberg, the father is Bernhard Blocksberg.
Both married when the mother was 17. In one episode Barbara and Bernhard celebrate their 15th wedding anniversary and in another episode Barbara celebrates her 32nd birthday.

By the way, at that time Barbara and Bernhard already had the same last name, because Barbara’s mother (Grandma Grete) is called Blocksberg, which means Barbara was already called Blocksberg before.
The series is still from the 80s.

The sister on the father’s side is called Paula Blocksberg.
Probably Barbara and Bernhard are cousins.
Bibi’s real name is Brigitte and in the first episodes she has a brother Boris Blocksberg, who is sent far away to the sea in one episode and does not reappear in future episodes.