If I void assault targeting my Yone and the enemies Rengar, moving Rengar to base and Yone to the battlefield Rengar was at, does Yone's passive trigger off Conqueror?

Yes, Yone, Blademaster's ability will trigger in this scenario.

According to RiftJudge FAQ #10336, moving Yone into a battlefield and simultaneously moving the only enemy unit out results in that battlefield becoming uncontrolled during the cleanup phase (before the showdown begins). When Yone then conquers this now-uncontrolled battlefield during the resulting showdown, his ability will trigger.

Sequence of Events:

1. Void Assault: You play Void Assault, moving Yone to the battlefield and Rengar to the base.
2. State Change: The battlefield becomes contested.
3. Cleanup Phase: During cleanup, because there are no enemy units there and no showdown is currently ongoing, the opponent loses control per Rule 187.4.c. The battlefield becomes uncontrolled.
4. Showdown: A non-combat showdown opens, and Yone conquers the now-uncontrolled battlefield.
5. Trigger: Because Yone conquered a battlefield that was uncontrolled, his ability triggers and is placed on the chain.

This is my interpretation based on the official FAQs regarding Yone's conquer ability and Void Assault. No official FAQ exists for this specific unit interaction beyond the established logic for how Yone and Void Assault interact with battlefield control.