Here is a screen shot of the basic layout of the Vintage B3 clone in Apple GarageBand and MainStage. A jazz Hammond organ player would want to be able to control each of these parameters in live performance. This assumes two keyboard manuals and a set of bass pedals. You may only be using one keyboard manual, in which case you would not worry about drawbar settings for the second manual or the bass pedals.
(A real Hammond organ does not have a knob for "distortion" as that is something produced by turning up the instrument's volume very loud. However, many "clonewheel" instruments add a "distortion" knob to simulate the sound of overdriven output into a very loud amplifier for hard rock and metal.)
Here is a screen shot of the "performance" layout of the Apple Virtual B3, showing fewer controls accessible. You would want to have at least these controls mapped to your MIDI controller keyboard. (although "organ verb" and "reverb" are optional and would be different for different virtual instruments other than Apple's)
(A real Hammond also does not have a setting for "key click"; key click is something that happens to a real Hammond when the instrument accumulates dust and dirt inside its mechanisms and they begin to wear out with age. However, modern players find that simulating the amount of key click with a control knob is desirable.)
There is one very important parameter not shown on this screen -- the expression pedal. It is operated with your foot, and it is plugged into the controller keyboard.
A Hammond organ player is almost constantly adjusting the expression pedal to create dynamic contrast in the sound.
So you need a MIDI controller keyboard that has an expression pedal input, and you need to connect such a pedal and use it.