Pick up Mac from repair with old owner info

[dreamsINdigital]

I bought a MacBook Air used from someone and brought it in to the store for repair. After I left and got the work authorization email, I realized that it had the previous owner's name tied to the device. Will this be a problem when I try to pick it up? Do you need to show ID when picking up a Mac from repair?

I went to My Support Profile (https://supportprofile.apple.com) to try to register it to my name, but it says it's already been registered. Should I contact the previous owner and have them deregister it?

Thanks