Go back to illusions for a bit.
Ignoring the metaphysics, which I, for one, believe, and at least some of the toughs must, as they keep a Chaplain on staff.
Kaff was taken off the stage. For a period of time, which ended up being four months, Kaff wasn't alive. Kaff was dead.
Ebby and Murtaugh may have been, no, WERE brain dead, but there was an Ebby and a Murtaugh right there in that medical bed. They were getting better.
From an outsiders perspective, Kaff died, as the placeholder that was identified as Kaff was gone, and nothing took its place for months.
From an outsiders perspective, Ebby and Murtaugh "survived", because their consciousness was reloaded into the placeholder that was identified with Ebby or Murtaugh. Even while they were brain dead, visitors could see "Ebby", or "Murtaugh", and know they were getting Ebby or Murtaugh back, just like before.
For a new thought experiment. Let's assume that morphing is fully possible and practical, but cloning is not. Let's also allow for brain copying and backup.
Say, for instance, that Murtaugh, feeling guilty that her side project cost Kaff his life, due to unanticipated, (by her), backstabbing disease, volunteered to be rewritten as Kaff.
So, four months after Kaff dies, Murtaugh is morphed to look like Kaff and has her, now his, brain rewritten to the thought patterns and memories of Kaff.
At no point does biological functions end.
When do you hold Murtaugh's funeral? The day she is reformatted into Kaff?
I don't have an answer to this. I suspect perception would be different for different people at different times. Possibly in a very short window of time, as people started to treat new-Kaff as Kaff, while mourning the loss of Murtaugh, then swinging to thinking of this as Murtaugh-Kaff, and only mourning that Murtaugh isn't the same person any longer and also mourning the loss of Kaff.
For another twist, let's say that Kaff decides to visit Haven Hive, but the trip proves too expensive. At the same time, Shep wants to hang out with the toughs. So, now in a double morph and restore, Kaff takes over Shep's body, and Shep takes over Kaff's.
I have my suspicions.
For starters, without the morph, there'd be a large number of people who wouldn't be able to see Kaff in Shep's body, and see Kaff, not Shep. Likewise, lots of people would continue to treat Shep as Kaff, while he was wearing Kaff's body.
When they swapped back, Schlock would make a comment about that being weird.
IF they also swapped looks, so Shep's mind, AND Shep's appearance were copied over Kaff's, and vice versa, things get muddier.
For the most part, I think people would treat them as they appeared to be, but be more comfortable when they swapped back, confident that the experiences they shared with not-Shep, or not-Kaff, were now legitimized by real-Shep, or real-Kaff, remembering the same events.