The name of the social security text message notification is wrong, but Alipay checked it. Is it a big impact?

Little impact. The incorrect name in the social security SMS notification may be due to the fact that the previous owner of the mobile phone number did not cancel the relevant information of the phone number in time. The social security system will assume that the two are the same person, but Alipay has performed real-name authentication, so there will be no error. You only need to change the name registered with your mobile phone number to your own name. The resulting inconsistency won't have a huge impact.