How to name new hard drive without conflict?
The name is relative and you can change it later. Just name the new drive new and use it for a week or day. Once you are ready to shift, name the old one "old" and put the name you want for new.

Or rename the old one before you introduce the new one.

This works out of the box, so I'm guessing you might have some other constraint that needs to be discussed, but perhaps you didn't know you could rename things on the go.

Also - never remove a working drive to swap until you’ve already set up the new drive externally and tested booting from the external drive. Then you know it’s bootable and working and if you put it inside, you know the fault is always the cable and installation - you don’t have to wonder if the OS wasn’t OK or drivers, etc...