After I become a US citizen and I obtain my Certificate of Naturalization, are there any other processes that I need to complete? I have heard that I might need to go to the Social Security office, why?
There are a few things you can do:
A website with more details about these, and other subjects like jury service, is newcitizen.us.
There are several reasons why you may need to go to the Social Security office after obtaining Naturalization in the US. One of the most common is that you are allowed to change your name when you become a citizen. So if you availed yourself of this you will need to change your name on all pieces of official documentation that you have.
Another reason would be if your Social Security card contains a notice: "FOR WORK ONLY WITH DHS AUTHORIZATION"(or similar), which you can apply for a replacement that won't have this printed on it.
Beyond that the only thing you may need to do is obtain a US passport.