Is there a special name for keyboards that only have a few keys?

From https://en.wikipedia.org/wiki/Computer_keyboard :

A keyboard with few keys is called a keypad.

https://en.wikipedia.org/wiki/Keypad:

A keypad is a set of buttons arranged in a block or "pad" which usually bear digits, symbols and usually a complete set of alphabetical letters. If it mostly contains numbers then it can also be called a numeric keypad.

If you have a few more keys, you could call it a 40%:

40% – Extremely small form factor with only the bare minimal of dedicated keys required to function. No alphanumeric keys, F-row or numpad. Many standard key operations will be hidden under multiple function layers. Some keys will be of a non-standard size.

Or alternatively, you could call it Apple Keyboard 2018.

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Example:

Why not simply get the standard 9-10 digit Numeric Keypad, cover up some of the buttons you don't use, and overlay a paper on top with actual buttons / instructions you do use? (Example as below):

This is the same method POS (Point of Sale) systems often used. They used a default keyboard, but pre-programmed each key for specific functions (or for adding pre-programmed items) and they overlayed the keyboard with a piece of paper (or maybe plastic-covered paper to make it somewhat water-resistant) with the correct program / function of the buttons.

If you want it to look better you can get your own custom-colored-printed-keycaps:

The reason what you wanted is expensive is because it is custom-built for a certain purpose. Anything that is not mass-produced is always more expensive.