I bought social security for several months without deducting money, and finally found that the name was wrong. Now I have changed. Do I have to pay a fine? How to calculate the liquidated damages?

What you said is not correct. There is no penalty interest for social security, because the base of social security is raised by 10% every July, which means that your original base is raised by five times. When you paid it back, the social security bureau calculated it according to the current base, so of course it will cost more than 20 thousand.

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