The tradition of the white wedding dress actually began when Queen Victoria wore a white dress to her wedding. Who knows if she was a virgin at the time 🤷🏼♀️ the idea that white wedding dresses are for virgins may have been created afterwards.
As for giving away the bride and the bride changing her name to match her husband's, originally that is about the possession of a woman moving from one man (her father) to another (her husband).
However, nowadays since women have a lot more rights and choices in life, the meaning behind these traditions is not as impactful. For example a woman might take her husband's name, but does that mean she is now literally his property? In the past, yes, but nowadays (and at least in socially progressive nations), no.
Feminism is about women being able to live their lives and make their own choices, without being oppressed in any way.
I consider myself a feminist, I got married and double-barrelled my name with my husband's, not with the belief of ownership/misogyny, but because that's what I wanted to do with my name. He kept his name as that was what he wanted to do with his name, and that's fine.
Changing one's name is a very personal decision and is not necessarily about bowing to misogyny.