This is a great idea, and in many ways in a return to a time when we were buried in shallow graves, unprotected from natural decomposition - so ecologically sound. There is a woman (and a team now) in Seattle moving forward on this idea. You might be interested in watching her recent TEDx talk: https://www.youtube.com/watch?v=PRsopS7yTG8 If the link doesn't work, look for "Life after Life" by Katrina Spade of the Urban Death Project. Also check out her website. This could be a reality sooner than we think!
A Mortality Coach is perhaps what I've always wanted to be when I grow up. but didn't know it. I wholeheartedly endorse the idea of being clear that this is a new kind of coaching, as opposed to life coaching. There is a special niche for helping people engage in their own mortality and take actions related to their own deaths that is not associated with "life coach".
I am a member of a "mortality group" that was spontaneously formed among a group of friends and is informally structured around thematic gatherings. I am 54 years old, but the majority of the members are young tech industry professionals in their 20's. I feel like there is surprising momentum, even among young adults, toward acknowledging our own mortality, so I say, Embrace This! and make the name straightforward and clear. I absolutely love "Mortality Coach". Even if folks you talk to today don't respond well to it, I'll bet they soon will as this trend picks up steam.