I think using it also stems from how you refer to your other half - for me I always say to the kids "Go see Daddy" for example - never "Go see *****" where ***** is his name, and he does the same for me, so then I think that links to you calling yourself in 3rd person sometimes. When my parents are here - the kids often start calling us by our names, because they hear them alot more from my parents when talking to me or DH, when is DH and I talking to each other, we don't tend to use our names so much as there is us or the kids don't need to distinguish who you are talking to so much.

It was around 2 that DD started not referring to herself by her name - I remember because we were doing "Who is that clip clopping over my bridge" and she kept saying "DD" and then suddenly she said "It's me - DD" and after that was a gradual progression to her saying "I". DS I can't remember, he still says "DS" occasionally I think.