This is ridiculous, there's a massive difference between taking your partner's suggestions into consideration and "changing for them". Not to mention that if you truly believe that changing your fucking HAIR changes "who you are" then you're the tool, hair is cosmetic, it is there for decoration and appearance only. If someone suggests a new style to you, it's not because they're trying to "change you", it's not because they don't like your current look. It's simply because they're suggesting an idea.
My girlfriend suggested that I might look alright with some facial hair, I've always shaved because I've never been bothered to try growing anything substantial. But I'm giving it a shot, not to please her, but because she suggested it could look good and I happen to agree with her, I might as well see what it looks like. That doesn't change who I am, that doesn't mean I'm bending to her will. It means I'm simply listening to her... Something any good boyfriend should do.