Depends what it was.

Would I change my hair color to make my partner happy? Sure, as long as it's not too drastic.
Would I wear my makeup differently? Yep.

I don't really see my outward appearance as defining. If it makes my partner happy, I would probably be willing to make adjustments to how I dress or look.
I wouldn't, however, become a different person to please my partner. If they aren't happy with my personality, why are they with me in the first place?
Then again, if it's just some bad habit I have my partner wants me to change, I would probably be willing to work on that, too. I don't think we can ever sit back and say we're perfect the way we are.
You should always be working on your "self". I would work on not being bossy, or nagging or things like that... but my partner should also be able to accept these things as a part of me and that it might not be possible for me to change.
Gotta accept the good with the bad, after all. Nobody is perfect.