I paid social security in Suzhou and now I'm going to work in Nanjing. Do I have to change my social security job?

Yes, job transfer and social security must also be transferred with work. You should first make a receiving culvert in Nanjing, then go to Suzhou with the receiving culvert to go through the transfer formalities, and finally hand over the formalities to Nanjing Social Security Center.

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