The sending Group Address of an Object is simply the first associated Group Address, in order to understand its role and importance: see here.
Changing the sending Group Address
If another Group Address shall become the sending Group Address then the ETS function 'Set Sending' can be used from e.g. the Object context menu (right-click).
No sending Group Address
It is simply not possible to have no sending Group Address for an Object, because of system requirements (i.e. the communication stack).