For the most part, when we're talking with Ethan about Vivian, we tend to call her Baby instead of use her name. Which is kind of funny, since she's almost as big as he is and she's almost 2, but whatever. I also use "baby" as a term of endearment when speaking to Ethan and Daniel.
Yesterday, Ethan finally had to speak up about this. He came up and said "Mommy?" and when I said "What's up, baby?", he looked at me with a very sincere (and slightly concerned) look on his face and said "No, Mommy, it's Ethan!" He's been saying it for a while, but it took me until yesterday to realize that he thought I was confused about who I was talking to and that he needed to remind me of who he was. Poor kid!
Daniel and I tried to explain to him that Mommy calls other people "baby" other than Vivian, and that her name isn't actually Baby, but I don't think he believes us :)