Hi Kate,
The probably issue which I could forsee is data getting wrongly updated into production if RFC connection from ECC to BW is not stopped.
Solution here could be to disable or deletethe RFC connections between ECC and BW before starting the SAP system at database level.
delete from sapr3.rfcdes where rfcdest = '<name>';
Once the system is up and running you can recreate them if required.
Also before starting SAP set the number of batch processes to 0 on the profile at OS level so that any released jobs don't start as soon as SAP is up.
Once the SAP system is up execute BDLS and change the logical system name.
Hope this helps.
Regards,
Deepak Kori