My fianc�e wants a double barrelled surname?

She said that when we register our marriage she wants a double barrel surname. Before I get into this I want to say that I know a lot of women see this as a feminist empowering thing where if a guy for any reason doesn't like this, he's cled as a misogynist. I'm all for women's rights. But I just feel when marriage takes place, the woman takes the guy's name as a sign of union. We're together as one so we have one surname. If she takes a double barrel surname, and we have kids, and they take their mother's name then I'm the only one without one, and to me it's just wrong. I tried talking to her but she said it's her decision. But Its a little heartbreaking for me and I don't know if I actually wants to be with a person who doesn't love me as much as I love them. What do I do?