I'm kind of planning to transfer databases from server1\instance1 (on
cluster-a) to server2\intance1 (on cluster-b) by detaching them from
server1\instance1 and copying to server2\instance2? Or maybe backing them
up to server2\instance from server1\instance1.

Will the fact the instance name (which I would very much like to leave
'instance1') is the same impede this process?

Thanks in advance.