Aloha, Paul, & welcome to the forum.
When you say kenjutsu, are you speaking specifically of kendo, or are you asking about iaido, too (or instead). If iaido, which ryuha?
I am not kendoka, but my wife has been studying kendo for many years, & she calls the one-on-one competition "keiko" or "ji-geiko." That isn't a formal match, though, but just daily practice. This corresponds with the two-person randori that I teach in judo, by the way.
In iaido (specifically Muso Jikiden Eishin-ryu in my case), there is no such a term, as we all practice against virtual opponents.
Maybe if you clarify your question, Paul, one of our other illustrious members can explain better.
Ken Goldstein
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Judo Kodansha/MJER Iaido Kodansha/Jodo Oku-iri
Fencing Master/NRA Instructor
"A positive attitude may not solve all your problems, but it'll annoy enough people to be worth the effort."