Hello
If the requirement is to display the image on all the screen to help the users in NOT getting confused, then I think it is time to educate the users in how to do their work effectively with 2 SAP systems.
The SAP GUI displays the hostname of the SAP system at the bottom right hand corner once you are connected to an SAP system.
If this is not sufficient in addition to the above proposed solutions then I don't think there is something which is exceptional in your case.
Good Luck
RB