Bunch, saying "a" in this context emphasizes that the secretary is not familiar with the person she is asking her boss about, in this case "Phillip Brainard." While she may say, "I have a Phillip Brainard waiting to meet you," or "There is a Phillip Brainard on hold on line three," what she is really saying through her tone and context is essentially, "I don't know who this person is, but he says his name is Phillip Brainard."
It is not a natural sound, but adding the "a" in this case adds a lot of meaning without saying all that much!