After meeting a III I got interested in nicknames and learned a thing or two. Here’s a quick list I compiled from people I’ve met and information I found on the intertubes and wikifacegoogles.

For the second: Junior, J.R., June, Chip, Duece, Two, Bud, <First name initial>.J. (e.g., Seth Jr. would be S.J.), Little <Name> (e.g., Little Seth), Younger <Name> (e.g., Younger Seth), Skip (particularly if the name skipped a generation), Sonny

For the third: Trip/Tripp, Trey/Tre, Skip/Skipper

Nicknames even extend to IV, V, and beyond! Maybe I would have learned this sooner if I lived with more WASPs in New England :) Have I missed any others?