How can I tell my parents I want to change my name?

So I'm a teen girl and I prefer the name Rory over my real name. It's nothing against my real name. I do think my real name is quite lovely but it reminds me too much of a time in my life that I would prefer to not have to ociate myself with. Ever since I was little I was forced to visit my birth father and I HATED it. Every time I hear my name called I just picture my birth father calling my name with his voice and thinking about times that I don't want to relive. He never did anything bad to me per say, he just didn't treat me correctly I guess you could say. Long story short, both my mother, step father, and the court agreed that my birth father wasn't fit to have any custody of me or be allowed any visitation rights. I've always loved the name Rory (no, not because of Gilmore Girls) and wanted to be called Rory for as long as I can remember. My mom really loves my real name though and I think it hurts her that I want to change my name. It's nothing against her at all, it's just that my real name has a lot of emotional baggage for me if that makes sense haha. I'm not trying to sound weird here and I apologize if it sounds stupid to anyone. When I go off to college I want to make Rory my legal name and that's what I want to officially go by. My stepdad wants to adopt me and I want him to as well so I'll be taking his last name and going through the adoption process in a few years. For now though, I'm just going to go by my real name so I don't hurt my mom's feelings. How can I make my mom understand that the reason I want to change my name is nothing against her, it's just that I want to be able to start fresh when I go off to college and not have to have the baggage of my birth name. And please don't just tell me to tell her this, because I've tried, but it seems like it hurts her feelings and I really don't want to do that because I love my mom so much. Sorry if this makes no sense to anyone and sounds totally dumb but I'd appreciate any advice.