Wow, that's such a lazy thought process. They clearly already have your social accounts. The vast majority of people are already linked to their parental units on some sort of social platform.
The point is, if they have your SSN, they know who you are. Or, possibly the person whose identity you've stolen with your fake credentials, but that's beyond the scope of this little thought exercise.
They have your accounts, pictures, SSN, yet only a partial name? Seriously?? They have your SSN for pete's sake. It's not like the gov't only stores a partial name with that SSN. The whole thing is a farce of an attempt to make it sound less than what it truly is. Your attempt at making it sound like it's not doxxing is also farcical.