All brands are different and generally do not work together. We are using Spektrum transmitters. Receivers we buy can be alternate brands, but must be compatible with Spektrum. Flight controllers do not care, but the receiver ahead of the flight controller must be matched to the transmitter.
The only thing to ensure between the receiver and flight controller is the method they communicate. A parallel bus with all channels connecting to the controller, or a serial bus with one wire connecting the 2 units.