Kimi Island and Shiromi Town are both named after a part of the egg:
Kimi is the reading of "egg yolk" (黄身).
Shiromi is the reading of "egg white" (白身).
Ironically, the roles of egg white and yolk are reversed, as the island is named after yolk, the inner part of an egg, whereas Shiromi Town is located on the island despite being named after the outer part.