Keeping the same serial number can help with software registration, possibly TM backups (or other backup software may use it), apple id logins for facetime/messages/icloud, so I would take the couple of seconds to copy/paste the values to the OC install.
It's probably faster to do a fresh install and copy over the home folder if you don't have a bunch of 3rd party software installed. The more software installed, the more it switches over to upgrading the existing install, as you don't have to track down serial numbers/install packages/etc...
When I was doing this, however, I did find it was easy to mess up upgrading and switching from Clover to OC, as IIRC, Clover copies some/all Extensions in the real extensions folders on disk, and those also have to be removed, as OC loads those extensions from the EFI folder without copying to the real extensions folders.
While I was building/testing my computer, I got it initially going on Mojave with Clover, but botched the job somehow switching to OC & upgrading that install to Catalina. Eventually, I just wiped it, and did a clean install of Catalina w OC, and that worked fine. And then later, once I was confident the computer was working fine, I copied over the Mojave install from my MacBookPro to the disk with OC, it booted fine, then upgraded it to Catalina (also fine), and finally to Big Sur 11.2, then 11.2.2,then 11.2.3), and it's been fine. I've got all kinds of software installed, and it's been working well for me.