The "Kathleen"

In "Danse Russe" by William Carlos Williams, the speaker of the poem adresses almost everything in a personal sense: "my wife," "my north room," "my mirror, "my shirt," "my arms" etc. There is a lot of "I" as well: seven in all. In the second line, however, there is "the baby and Kathleen." He does not refer to the baby as his own. The baby may not be his. If it was his baby, however, why would he refer to him/her as "the baby"? This poem is quite like the speaker escaping, at least in a mental way, his own life--being "lonely" without the others intruding in his life. It may be that the baby was impersonal for that reason. Same could be said for "Kathleen" too. The one thing that makes peculiar about "Kathleen" is that, that is the only proper noun written in this poem. The speaker, his wife, nor the baby had been identified with names. If she was his daughter, he could have written "my daughter." If it was a servant, he could have written "the servant." If it was his dog, he could have written "my dog." What was the meaning of this queer creativity? Although the speaker does say that he is "best so" at being "lonely," he could possibly be reaching out for someone to grasp his hand and tell him "no." He may be pointing out that something that one may think is the "best" may not be, and the person may be longing something else--something else that he/she may not have noticed--reaching out for it unconsciously.