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...I went to review the information in my support profile and noticed my name isn't shown in the return shipping address section on the repair status screen. It just shows the street, city, state, zip, and country.

Is it normal behavior that my name isn't shown?

Don't worry. It isn't shown in the emails I got from them on this issue either. Only street, zip, city.
 
Regarding this program, I did this for my sister's iphone way back in early September and they gave her a brand new phone. I think it may have still been under apple care plus, though it did not count towards any replacements, if it indeed was still under apple care.
 
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