I was half-right; It's a filler but he has no name yet.
Panel 1: Mike puys the puppy into his cage and tells him that this is his new home.
Panel 2: Elly explains that she's put one of his old stuffed toys and John's old T-shirts in there with him. Mike asks why.
Panel 3: As we see the little thing stare at them, she says that he needs something soft to sleep with and familiar to smell to calm him down so he can sleep. Mike responds with a muted "Oh."
Panel 4: This is why we see Mike clutching onto one of John's shirts when HE sleeps.
Summary: Tomorrow, we have to deal with the reprint.
ETA: This strip and the one that follows are meant to send a message: John would rather be with the dog than his kids. This is meant to be another slam against Rod but when you remember what they become, who can blame JSF?