Notice that Charlie Brown calls Snoopy "that dog."
He still hasn't been named yet.
Once again, the joke is a simple visual gag borne of subjecting kids to the trappings of adults. Why would CB wear an adult's tie? But there's also the strangeness of the situation. How could this state of events have come about?
EDIT: karlosthejackal notes, in the comments, that Snoopy was named in the past. Thanks ktj, I should take better notes!