If Genku and one or more other nontoken permanents you control leave the battlefield at the same time, Genku's ability will trigger for each of those other nontoken permanents.

If multiple other nontoken permanents you control leave the battlefield simultaneously, you must still choose different modes for each instance of the triggered ability that's put onto the stack. If more than three other nontoken permanents you control leave the battlefield simultaneously, that choice is made only for the first three.

If you can't legally choose a mode because all three have been chosen that turn, that instance of the ability is removed from the stack with no effect.

If you somehow control two or more Genku, Future Shapers, track which modes have been chosen each turn for each one's ability separately.