Timing of the name change truly depends on how you go about each step of the process.
For example: The first step will be updating your name with the Social Security Administration. If you go in person to submit the application we provide, you'll be able to begin submitting other applications 48 hours after the time of your visit. If you submit the application in the mail, you'll need to wait until you receive your new Social Security card in the mail (about two weeks) before submitting any other applications.
Generally speaking, you should be able to complete the entire process anywhere from 2 weeks to 2 months.