andycarmenjapanese8100-san,
no, they don't have to
It's a very interesting and good question! Some parents might give names related to the season babies were born, but
it could be for some other reasons, like "because I want my child to be bright and shiny like summer sun" or
simply "because I love winter"
Names like Haruko, Natsuko, Akiko and Fuyuko might have seasons in their names, but depending on what kanji
they use, it might have nothing to do with seasons. For example my name, Natsuko, doesn't have kanji for
summer as you see below.
Japanese names are interesting, isn't it?
Natsuko(奈津子),
Team JapanesePod101.com