select, choose, surname
遴 centers on the act of carefully selecting or choosing, often with deliberation. The surname sense is a specific application of this idea.
遴 combines the movement radical 辶 with 粦, which likely contributes the sound. The exact historical development of 粦 is uncertain, but the character is associated with selecting or choosing, possibly from the idea of moving through options.
The movement radical 辶 surrounds 粦, like walking around a set of options to carefully select the best one.
For リン, imagine a careful selector named Lynn who walks around the options: Lynn -> リン, and she chooses the best one.