Thus, slowly and slowly vanishing the name of Senju clan but the actual members of this clan may be good in number. In my opinion, Moegi Kazamatsuri awakened and inherited the wood release due to being a descendant of Hashirama Senju. Also, the reason these children bearing their mother’s surname could be that the Senju’s left their mother’s after the child was born and hence no mother named their child a Senju.
Also, in my opinion, she is not just another experiment or a test subject of Orochimaru like Captain Yamato. Yamato who is a famous Jounin and a former Anbu Black Ops member of Konohagakure. He was the team captain of Naruto’s Team 7 as well for some time. Also, if Moegi Kazamatsuri was a test subject of Orochimaru then she would have been on the radar for some time. And when Konohamaru, Moegi, and Udon were born Orochimaru was already on the run and was focused on getting a new body for himself.