All of my children (3) went through a brief phase around the same time (age 4, such an endearing phase in any child's overall development), of calling me by my given name.
I never made a big deal out of it, nor did I pretend not to notice. I just very naturally responded with a mildly surprised / quizzical look, as if thinking, "you usually call me Mommy, because you're my child, not an adult friend...I'm a little confused and a bit amused by the way that you address me these days." But certainly not the slightest bit shocked or upset by it.
I was careful not to over-react, which would tend to confuse and traumatize them. They don't really understand why they do such a thing. They act intuitively, subconsciously, and with noble intent. I would never intentionally spoil their happiness and their deep and abiding trust in me. I would never deliberately ruin the affection we had for one another.
Being that my children were quite sensitive and intelligent, and considering the close bond we had, they easily recognized my nonverbal response for what it was. There was no need to lecture them or to explain manners to them, in that regard (not that I would never do so, but in this case it was unnecessary, because I instinctively knew that they'd quickly grow out of it on their own, as long as I handled the situation diplomatically).
It took them only about a week at the most, to self-correct and revert back to the more familiar "Mama" or "Mommy". I doubt any one of them ever called me by my name more than about five times, total. And that's a conservative estimate, as it was probably even less than that.
I understood that my children were testing our boundaries, and on some unspoken level I felt somehow proud of them and honored that they thought enough of me to experiment with the quality of our relationship. They were always respectful, and I never feared that they would get out of hand. They were obviously just trying to be sociable with me, and I took that as a compliment without calling excessive attention to it.
Neither did I encourage it, however, which they also recognized subconsciously. But we always communicated very openly and respectfully, and I'm sure that if they asked me about it ("Mommy, can I call you Bread?" :D ) I must have said something like: "I don't mind if you call me by my name, because we both understand that I'm your mother and you're my daughter / son" (If indeed they did ask, the ensuing conversation was very light and brief, their place in my heart reinforced -- then on to more interesting things in a child's life, like play, food, and friends.)
By taking it all in stride, while remaining calm and caring toward them, and maintaining a gentle sense of humor about it, involving us together as a family (rather than laughing at, embarrassing, berating, or mocking them for it) -- I did my best to help them progress through an important developmental stage with their self-esteem wholly intact:
Psychosocial Stage 3 - Initiative vs. Guilt The third stage of psychosocial development takes place during the preschool years.
At this point in psychosocial development, children begin to assert their power and control over the world through directing play and other social interactions.
Children who are successful at this stage feel capable and able to lead others. Those who fail to acquire these skills are left with a sense of guilt, self-doubt, and lack of initiative.
When an ideal balance of individual initiative and a willingness to work with others is achieved, the ego quality known as purpose emerges.