Well, in a sense
Brynn never "switched genders" in the USA because it's been predominantly female ever since its introduction here.
The original popularity of
Brynn as a female name in the USA seems linked to the career of actress
Brynn Thayer while she appeared as the character
Jenny Vernon on the daytime soap opera
One Life To Live between 1978 and 1986.
Brynn seems to be her real first name, not a stage name, but so far I can't find any explanation for why her parents chose it.
http://brynnthayer.com/