Good question. Under the assumption that Yamamori survives the conflict it seems fitting that his family also survives as a final reflection of his change in luck. The family has a military history with the SLDF and the TH and remaining on their home planet of Earth would seem to be a great weight. So I expect that he and his family would join the Exodus.
It's unclear at least from the Battletech Wiki whether all 803 names have been defined yet. The note there says:
"List of Bloodnames, Including Non-Exclusive
Below is a list of greater than 450 identified Clan bloodnames, listed in alphabetical order and unsorted by Clan or service. Please note that 803 bloodlines existed immediately after Operation Klondike, and through Reaving and (rare) additions, 682 exist prior to the Annihilation of Clan Smoke Jaguar"
The site lists 484 Bloodnames still active and another 58 eliminated. How many undefined names depends on the specific Clan. If there's a better source that's more complete I'd appreciate it.
If there's a complete list, I've considered what that means with regard to the lack of a Yamamori bloodline within the 800 from the clans and I see a couple of options. The first is to simply not worry about it as we're not trying to write cannon here. The alternative is for Yamamori to change his name. As the younger son, he's not as critical to carrying on the family name. I can easily see circumstances where his mother's relatives have died and there is no one to carry on that name. To honor their sacrifice and to ensure their name lives on in blood relatives, he would take her name. At that point any Japanese last name of the bloodlines without a cannon founder becomes a viable option to have been Kenji Yamamori.
As a variation on the theme he could end up marrying and taking his wife's name, again providing a way to change names while remaining true to the character. Both options works within the scope of things.
This is my current thinking, though that could change depending on what happens over the next couple of sessions.
With a sweep of his...
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