My mom changed her name when she was in her 20s. Nothing drastic, she just combined her first name and her middle name.
She said she regretted that - not sure why, she just said it was a spur of the moment thing. Nobody ever calls her by that anyway - I don't think most people even know about the second half of her name.
Anyway, I like the name Margaret, but McKenzie (that is your first name, right?) is pretty, too.