I'm upgrading the receiver on a remote-controlled ceiling fan unit (which also controls the ceiling lights in that room). The wiring diagram changed from the old model to the new -- most importantly, the white common wire not connects to the white neutral-in wire. Would I do that with a simple twist-on wire connector, or is there a better way to do this?
In US 120 volt household circuits, all neutral (white) wires on a given circuit are ultimately connected. In your old receiver, there was almost certainly a direct connection between the white in and the white out, as well as a connection to the receiver circuitry.
Connecting all of neutral wires (source/receiver/canopy) with a simple wire nut is fine.