The household registration book shows divorce, and you can get a marriage certificate. Although I am in the same household registration book as my ex-husband, but now I am married to someone else, I can move my household registration to my current husband's household registration. If you remarry, as long as you don't register with the registered police, it won't be displayed in the original household registration book.
Legal basis: Article 10 of the Regulations on Registration of Household Registration in People's Republic of China (PRC), if a citizen moves out of the jurisdiction of the place where the household registration is located, he or the head of the household shall apply to the household registration authority for registration, obtain a transfer certificate and cancel the household registration before moving out.