Dear Afternoonan,
If the computer is already member in specific collection and you implement refresh scenario, the computer will still the same but I think you are re-booting the computer and using a new scenario (Unknown computer) the name will be random.
I hope that this is answer your qustion.
If you need help to create TS and advertise it to collection plz let me know, after advertise wait for notification then TS will run and the computer name will be the same.
Computer Name will change only in case you advertise TS to Unknown computers.
Regards