How to name new hard drive without conflict? I have a MacBook Pro with a single SSD installed - the disc is called “my favourite name”

I just purchased a new larger ssd which I want to install instead of my old ssd.

When I format the new drive can I name it “my favourite name” ? What happens if I try to use migration assistant to migrate files from my backup of my old ssd called “my favourite name”?

How do I successfully transfer my files, and ensure my new ssd is also called “my favourite name”

Edit: just to clarify - this is a laptop. I remove the old drive and install the new.
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...