I make my pools with the serial number /dev/disk/by-id/ names, like ata-WDC_WD30EFRX-68EUZN0_WD-XXXXXXXXXXX.
That is not going to change between different machines as far as I know, I might be wrong about this. I made some bad choices (in hindsight) when making this pool for my uses, but it's still going strong many years later. [1]
This current pool (which is now old, 50k+ power on hours on these disk) has survived a motherboard dying randomly and one or two SSD failures with the OS on.
Always just installed a OS on a new SSD and it's been picked up just fine.
[1] I went with RAID-Z2 for 6x3TB WD Reds where I probably should have made mirrored pools or something like it to gain more space? It's been a while since I looked at it. Can't really expand this pool or add more storage without replacing each disk one by one with something bigger.
I could make another pool with new disks but I'd lose another 20% to parity.