check, examine
檢 centers on careful inspection: checking or examining something to verify its condition or truth.
檢 combines 木 (tree/wood) with 僉, which likely contributes the sound and the idea of gathering or checking. The character originally referred to a wooden tally or seal used for verification, hence the meaning of checking or examining.
A wooden 木 tally 僉 is used to check and examine records. Picture an official holding a wooden slip up to the light to inspect it.
For ケン, imagine Ken the inspector carefully examining a wooden tally: Ken -> ケン, and he always checks twice.