For a game-play simplicity standpoint, I like the part of only having one character with each name per island.
Having said that, I think that relaxing the name change rules to allow a minor change in order to allow a character to emigrate should be acceptable. The idea of only allowing certain name changes is to prevent people from changing their name at will, and thus attempting to hide from their history with a simple name change. But if you're changing islands, why not allow the addition of a middle name to differentiate so they can move?
