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Changing your name should be your choice, not your parents'. Don't let them influence what you do. You are old enough now to think for yourself and make your own decisions in life.
But I'm sure you can understand where your mother is coming from and why she's so against you doing this. I mean, I'd be heartbroken too if my daughter decided she wanted to change the name I spent hours picking out for her. This is something you can understand, yes?
But if changing your name is something you really want to do and you're positive you won't regret it twenty years from now, I say go for it. Remember that it's your life to live, not anybody else's. Your parents can't tell you what to do anymore.
Linda sounds kind of middle-aged to me; it's hard to visualize the name on a baby girl. But I don't think this should stop you from using it. There is absolutely nothing wrong with Linda. And if you like it, then you should use it! But maybe consider alternatives like Lindy or Lindsay first.