That was a tough one...
My kids were 5 and 3 when I started living full time... I involved my ex-wife in the decision as her support would be necessary in the matter. We knew it was going to be an issue after a night at Golden Corral in a place I'll call Redneckville, FL. My daughter came running up to me, so excited ... "Daddy!!! They have pizza!!!" It was like a scene from an old western when everyone stopped what they were doing and turned their heads in unison. I talked to my daughter, the five year old, about it.....
I told her that I would always be her Daddy, no matter what. I said that calling me Daddy in front of other people,though, would get them confused because I was a girl now. As most kids do, she understood completely. We tried using "Daddy" in private and my first name, "Jess" in public. Over time, it evolved to calling me, "Jess," all the time. My son followed suit. They're 7 and 4 now... They never refer to me as, "Daddy," anymore. It's the only part of being male that I really miss. That was probably the hardest part of my transition... knowing that my role as a parent was changing forever and that there were certain facets of the relationship with my kids that were always going to be, "alternative." They sometimes say that they miss, "him." I think that, after carefully considering the context of the statement, they're really saying that they miss Mommy and Daddy being together and us all living in our old house.
On the flip side, I feel that my ability and effectiveness as a parent has improved dramatically since transition... I'm not withdrawn and depressed anymore, the weight of being in the closet is gone. "Jess," is just what they call me... They KNOW I'm their parent no matter what the label.