Sorry to disappoint you, but from my understanding, you cannot upgrade on an AA ticket even if its a CX codeshare as your PNR is under AA's PNR and not CX. Don't know how the CX agent thinks that you will have a CX PNR ??
There is no CX reference on the AA ticket until literally 24 hours prior to departure when AA hands over their bookings to CX. When you mean CX codeshare you mean that its an AA ticket on AA metal but CX flight number? Or do you mean that its an AA ticket on AA flight number but CX metal?
Either way, name shouldn't matter. Depends on who booked the ticket and how they input the name.