big-mouthed flounder
鰜 centers on a specific type of flatfish: a big-mouthed flounder. The meaning is narrow and concrete, referring to this particular fish.
鰜 combines 魚 (fish) with 兼, which likely contributes the sound. The exact historical development is uncertain, but the structure is a typical phono-semantic compound for a fish name.
The left side 魚 means fish, and the right side 兼 looks like a hand holding two things together. Imagine a fish with a mouth so big it can hold two things at once, like a big-mouthed flounder.
For ケン, picture Ken the fisherman catching a big-mouthed flounder: Ken -> ケン, and the fish is the 鰜.