So the basics are, Olga is the daughter of Sergey Sukhoruchenkov, the two-time Peace Race winner, Olympic road race champion and two-time Tour de l'Avenir winner widely regarded as the greatest climber the Eastern Bloc ever produced. However, he and Olga's mother broke up and she never took his surname, instead keeping her mother's surname growing up, and they never really knew each other until Olga was 16.
Olga was previously married to a cycling coach named Yuri Anoshin, and their marriage was apparently current when she won her Olympic medals in 2012 as she namechecks him in articles during the Olympics. She had two children prior to this (Bogdan in 2004 and Vitaly in 2008) and a third (Evelina) in 2013. It seems that soon after this, however, the couple broke up. I anticipate this is probably why Bogdan has his mother's surname.
Sergey Klimov ran RusVelo in 2016-17 and Cogeas women's team from 2018 onwards, with Zabelinskaya riding for them from 2018 onwards. Not sure if this union is because of them having already got together or if they became close while working together at the team. I can't really square how we get to her having two children with Klimov out of 3 when 2 predate the Olympics when she was with Anoshin. The most likely thing I can think of is that if they didn't marry until 2021, after Bogdan was already 16, so he was not considered a child anymore in Russia.
Either way, she took up the Uzbek licence to compete in the Olympics, because she would have been otherwise prevented - she has a positive test from 2014 in her back pocket and her competing in Rio was already controversial as she'd only just returned from suspension. Since the family have been resident in Cyprus since 2018, Bogdan has qualified for Cypriot nationality on residence rules and taken it in order to be able to compete at World Championships, Olympics and other administrative benefits given current sanction status of Russia.