Name Changes

I know it's a little early to think about it, but I just happened to be looking at my social security card and realizing that it has my current name on it. I know how to go about changing my name on my drivers license, passport, credit cards, etc., but what about social security card? Is that something that I have to do or does the government just sort of know and send me a new one with my new name once the marriage license is filed? Or does it stay the same since most things that you would need it for one could state that it's your maiden name?

And while I'm on the subject, what about student loans? Or does that really matter if the name isn't identical since the SSN matches and I'd still be paying?

TIA!!!!