It's possible to operate Z strategies in Darwinex through MT5 while having other EAs running. Is it necessary to modify the assets file in case the indicator names are different?

Yes, but not on the same chart. You need the zorro EA in order to receive price data and send orders.

The asset list file is only about all things related to the given asset.

More details on https://zorro-project.com/manual/en/zsystems.htm and https://zorro-project.com/manual/en/account.htm