raise, lift up, surname
揭 centers on lifting something up physically or metaphorically, such as raising an object or hoisting a banner. The surname sense is a specialized application of this raising idea.
揭 combines 扌 (hand) with 曷, a component that likely contributes the sound and may relate to lifting or raising. The exact historical development of 曷 is uncertain.
The hand radical 扌 beside 曷 suggests a hand lifting something up. Picture a hand raising a heavy object with effort.
For ケイ, imagine a hand lifting a heavy key: key -> ケイ, and the hand raises it high.