This is a noob question, please don`t be too harsh on me. I would like to use a motor for turning a mixer. The shaft of the mixer should be removable and I though of 3d printing a case which holds the motor and a gearbox in place. I made a very simple drawing of how it should look like (or how i can imagine it). I was wondering if such a thing already exist but I do not find it because I do not know the name. It should be easy to remove the shaft. Some sort if quick release/fix. The motor will run at 300 to 1000 rpm at low torque.
Most general purpose gearboxes will have a fairly short stub shaft which is connected to the main shaft by some sort of coupling. Exactly how this is implemented will depend on the application.
Light duty couplings might just be a collar held on with grub screws or cotter pins heavier duty applications may use keys or splines. Splines are often preferred if the shaft needs to accommodate some axial movement and for very heavy duty applications such as vehicle transmission.
The version you have drawn has the added complication that a completely removable shaft needs to accommodate both the final drive gear and a set of bearings with a pretty good fit.
One solution would be to have the final gear running on a hollow, internally splines shaft but this would be rather complex and expensive to manufacture. There is also the consideration of keeping the gearbox internals reasonably well sealed to keep the grease in and any dirt and grit out.
In practice many mixers with removable blades are similar to electric drills, using a chuck or similar quick release mechanism to allow easy fitting and removal.
A basic 3 jaw drill chuck will transmit moderate torque to a round shaft and somewhat higher torque to a hexagonal shaft and they have the advantage of being cheap and easily available.