I really like capability systems, but 'capability' is a terrible name.
In normal English, a capability is something intrinsic. If you have the capability to run a four-minute mile, it's something that you can do. You don't need some token to enable you to do it.
In a capability system, holding a capability doesn't grant you the ability to do the thing implicitly, it requires you to present the authorising capability when you try the action. This is one of the core advantages of capability systems over other kinds of access control. They respect the principle of intentional use. It's not enough that you have a capability to do a thing, you must use the correct capability when you try to do the thing. This eliminates a whole set of possible confused-deputy attacks.
Capabilities are more like inventory items in an adventure game. Just having them in the inventory doesn't let you solve a puzzle, you must use the correct inventory item on the correct object to solve the puzzle.
I can't think of a better word. 'Tool' might work (except that it's almost as bad as that time some French people named a theorem prover). Saying 'I don't have the right tool to accomplish this task' makes sense in English as a 'I need to hold this thing and use it correctly', whereas 'I don't have the capability to accomplish this task' sounds like you're talking about ambient authority.
Are there better words? Maybe something in another language?