In Genesis one of the "jobs" Adam is given is to name all the various animals in the Garden. When we give something a name we take the first step into bringing it into "personhood" because we have singled it out and given it an identity and communicated to it making it apart of a community.
Personhood can only exist within a community. For instance if you were the only 'thing' that existed would you really exist? We only exist in as much as we communicate and interact with other people or when we begin to develop personality. This is a major part of the doctrine of the Trinity. My point is that Man was given a purpose to bring creation into "personhood" to a certain extent. Some of the Church Fathers speculated quite a bit about this, especially St. Maximus the Confessor. I have come to believe that as the Logos is the mediator between God the Father and us and we are in the image of the Logos we are to act as the mediator between God and the rest of creation as we are its highest aspect and to ultimately bring the rest of creation into personhood. To some extent.
So to answer your question I dont believe God has a name for us as he left that up to us.
