Hello Diana,
If you want to maintain system alias in PROD system .you would require PROD edit access i.e PROD system need to be put as "Client Open" (it means PROD system need to put in change mode). Always PROD system with display access only So because of this reason it is asking customizing request to add system alias. Check with BASIS team to sort out the issue.
If they agree with option "Client Open" or any other option like to edit you can add the system alias without any customizing request otherwise you have to transport it from lower levels.