Question about Marriage License and new last name....

What is the deal with the marriage license and the last names? Is his last name now my legal last name? OR is it not my legal last name until I change it with Social Security? I am so confused. How does this work?

Someone said that The Town of Brookhaven is the only one who recognizes me as the new last name...

Anyone?

The marriage license is proof that you are married and that the way you listed your name after marriage is the way you wanted to be called.

Officially though it's the SSN that will be the final name change. Cause everything you put your SSN on will reference that name.

Make sense?