Rouge, if you enjoy the relationship and if it's healthy for both of you, I can see danger in trying to over-analyze the whole thing. Maybe you continue to call her Dr. X because for you that's her name. It's what feels normal and natural. It may be true that the friendship may not have reached a point yet of being on totally equal terms. Instead it may have morphed into something like Big Sister and Little Sister. Keeping that dynamic can have a certain comfort. Speaking as both a Big Sister and a Little Sister, I know how natural it feels to stay in that role as long as all parties feel okay about it.

I maintained a long-term friendly and professional relationship with one of my mentors for years, until he passed away. Let's call him Dr. J.B. Smith. His professional colleagues called him J.B. His close inner circle used his inelegant given name. Very few people knew his given name. In public, his inner circle also called him J.B.

He'd call me up and say, "Hi, this is Jimbob." And I'd respond, "Hi, Dr. Smith."

When he sent email or letters or other communication, he always signed it "Jimbob." When I wrote him, I always said, "Dr. Smith."

To me, his name was Dr. Smith. It felt right to me. He didn't seem to mind.

This is my theory: By using Jimbob, he was giving me admission into his inner circle, which was a small group of comrades. He was acknowledging I'd grown out of the student role and into a more mature, equal role. I called him Dr. Smith out of respect and as a way of acknowledging the reality that in many ways he was still my mentor. He had much more life experience and professional experience. We were friends. There's no doubt about that.

When I felt especially relaxed, I'd call him Dr. S. What mattered was the quality of the friendship, the reciprocity and give and take. He had strengths I didn't have and I had strengths he lacked. We didn't give each other identical things emotionally, but we both gave the same amount, sometimes more, sometimes less, depending on circumstances, but it equaled out over time. We complemented each other. It worked.

If your relationship is healthy and if you're both giving as well as receiving, even if you're not giving the same things, if you enjoy each other's company, it may not matter what you call her. Just as long as you call her ... just for the sake of friendship.

I wish you the best in figuring this out.