Does renaming affect social security?

That's true, but it doesn't matter if changes are made in time. After the identity document is renamed, if your previous name is found in the household registration book, take a copy of the original household registration book. If you don't have your previous name, you should go to the local public security organ to issue a household registration certificate and take the materials to the social security department for change.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.