Yes. After you get married you will need to change your name through the Social Security office. When you fill out the paperwork put in the new name that you want.
Make sure to review the requirements from the Social Security Administration. You will likely need to bring in some sort of picture ID with your maiden name and then a certified copy of your marriage license. Please note, however, that if you want to add a hyphen (Perez-Ramos instead of Perez de Ramos) this will require to file an official petition of name change in the courts. Also, once you have changed your name, make sure that you change other identifying documentation such as your driver's license and passport. This will require you to go to the department of motor vehicles as well as obtain a new passport. Good luck!
This answer is being provided for informational purposes only. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship. For legal advice relating to your specific situation, you should contact an attorney and arrange for a consultation.
The short answer is yes but I would recommend contacting Social Security at 1-800-772-1213 to make sure what documents may be needed to make the change. Best of luck to you.
This information is provided as a public service to provide a general answer and should not be relied upon as legal advice.