It's a good idea to think about brand as what our markets think about us. By our markets we mean both those who use the value we provide and those who could use the value we provide.
So certainly we can have brand intention about what we want people to say about us behind our back.
Many organizations look at mission as the business for him which translates basically into brand. This includes both our actual brand as perceived by the market and are intended brand.
One way to look at mission and vision is that mission is our current brand as it exists and vision is our intended brand. This makes for an easy and simple distinction which helps guide us in putting together our Agile Canvas.