Alternately you might say you are transferring the service to another person? Success and ease might depend on the type of service and reasons. Any sign that the Telstra support does not respond as if the request is a routine and everyday item for them should send alarm bells ringing.
We have done it several times between business and private, and once to business. Lots of paperwork and proof of identity. Some older Telstra accounts were in a legacy system which may or may not be relevant to your needs.
In each instance Telstra issued new account numbers as the identity of the customer changed. It has been a right Royal P in the A as they say. Experience from previous two years.
Never again. We’d now ask to close one account and open a new one, unless it was a simple transfer of a mobile service, private to private. We have done this in the previous two years with Telstra mobile and for a different instance with Optus mobile. Minimal pain with Optus.
For the one other instance where there was a deceased partner the change occurred ten years ago. In those days you could still get service and it was not too difficult from memory.
No cost for any of the changes!