I always find it interesting that many parents in my classes want their children to write their name by the end of the school year.
If you were asked to remove one shoe and hold a pencil between your toes and write your name, could you do it? Writing is an acquired ability and it is as difficult for young children to control a pencil in their hands as it is for you to control it with your toes.
As your teacher, I could help you develop your toe muscles, for example, by allowing you to manipulate play dough or clay with your toes.
Since the start of school, the children in my classroom have regularly played with the materials in their environment to develop the fine motor skills necessary for writing. So what may appear as play to parents is actually active learning, giving each child the opportunity to be active, rather than passive learners, and to foster creativity, initiative, and spontaneity.