Okay, second take.
If Bayushi Saya targets another player's personality who then either assigns to attack or uses an ability, can Doomed Intentions be used to kill that personality?
Saya + Doomed Redux
A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
Reaction: After another player's action resolves that dishonored any of his own Personalities: Destroy one of those target Personalities.
I fail to see how your Bayushi Saya dishonoring another player's Personality for attacking or performing an action meets the requirement of, "another player's action resolves that dishonored any of his own Personalities."
Doomed Intentions only works if the player's Action causes the Dishonor itself, not whenever one of your Dishonor effects triggers off of his Action. Also, "Assigning to Attack" is not an Action.