Actually yes, you would be able to rename the new pool to the old name.
It can be complicated at times, because the Shares use a specific path. Thus, renaming can be useful. However, it is not a common task so I don’t know if that is in the GUI.
In this case however, you’d be replicating data01 to temporary data02, and then creating a new data01 pool and replicating from data02 “back” to data01 so renaming should not be necessary.
Renaming is not in the GUI, but of course it’s straightforward enough from the shell: zpool import oldname newname. Then export it, then use the GUI to import it. A little tedious, but not particularly difficult.
In the end, I created a new pool with the 2 4TB drives as a mirror, replicated the old pool to the new pool, deleted the old pool, re-created it and replicated again the other way, and I think it worked (or I’ll have a very bad surprise at some point ). Thanks again for the tips and help!