Can a stipulation be made in a Custody agreement that requires a parent to not use a nickname for their child?

I have a child (19 months old) with a woman who chose a first name specifically because she knew I didn't care for it. Because of this I refer to my child by a nickname (unless at a doctor or a place of formality). The nickname is not offensive or detracting, it is a shortening of the child's middle name. I will not use the real name here, but think along the lines of if their middle name was Robert and I called them Robby. The woman and her lawyer claim that they are going to push to have the custody agreement written such that I am no longer allowed to call my child by the nickname because it is "confusing to the child" and it would be okay if the nickname was "Smiley" or "Pumpkin" but because it "sounds like a real name" it is detrimental to the child. Is this possible?