The name of the second-hand house I bought hasn't changed.

Legal analysis: it is recommended to go through the formalities of renaming. It is not clear whether the ownership of the house is confirmed. If a third person buys a house from the owner (seller) and registers it, then the house will eventually be owned by the third person instead of claiming compensation from the seller.

Legal basis: People's Republic of China (PRC) City Real Estate Management Law.

Article 36 When transferring or mortgaging real estate, the parties concerned shall register the ownership in accordance with the provisions of Chapter V of this Law.

Article 62 When a real estate is mortgaged, it shall be registered with the department designated by the local people's government at or above the county level. Where the land use right and house ownership are obtained due to the disposal of mortgaged real estate, the transfer registration shall be handled in accordance with the provisions of this chapter.