friendship
Nicknames -- or the use of nicknames -- need to be earned in my opinion.
you are the advice columnist
The name fits me less than it did before, and no amount of asking will get them to stop.
dating
A friend and I once made a conscious effort to stop referring to her flirtatious colleague as White Guy ("God, why do I call him that? You know I'd die if he were referring to me as Black Girl," she kept fretting).