There are websites with the 100 most popular names in Japan by year, but they are in Japanese. I've looked at them and none of the girl's names sound like "Shawn." I can assure you that there has never been a popular Japanese girl's name that sounds like Shawn, Swan, or Dawn.
About the closest one can get is Shion, which is pronounced "shee-own."
Please excuse my being rude, but since you've posted repeatedly about a Japanese girl you met whose name sounded like Shawn, are you absolutely sure that this individual you met was Japanese and not some other nationality? If she was definitely Japanese, do you have reason to believe her name is popular in Japan or could it be a rare name? Could it be an English name that she was using in place of her Japanese name?