Drop a last name on social security?

On my social security card it shows that my name is Juan Antonio Sanchez Garcia. My real last name is Sanchez but my mom added her madden name to the end of it. Now that I am 16 and started to work I go by Juan Garcia and i dont want that cuz sometimes it is a hle at the bank and my mom has to cash my checks, also my license does not have garcia but my birth certifiacte does. I did some research and it says i had to change it on birth Certificate, but I was born in Mexico. Right now i dont have time to go and change it is there another way I can go around that.