I registered for applecare under the wrong name.

Hi , i recently registered for applecare and i chose to receive the comfirmation of if i had registered sucessfully by mail . Today , i received the mail and to my shock , it was registered under the name " Joshua Lim ". That is certaintly not my name and im afraid that if i go and claim my protection if my mac breaks or something , the will ask for my ID and the two names will not match up , making my protection plan void . Will the plan still be valid if i dont change the name ? If it isnt valid , how can i change the registered name and / or make the plan still work . PLEASE HELP😢 Urgent .