You can first register a notification chain in your kernel module.
Inside get_signal_to_deliver( kernel / signal.c ), any process that has just (the relative term IMHO) has been killed has the PF_SIGNALED flag set . Here you can check the name of the current process using its tcomm field, for example:
char tcomm[sizeof(current->comm)];
get_task_comm(tcomm, current);
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