Bando shows up in the 12th chapter, titled "In Which I Find a Real Live Man." Sam hears a police siren in the distance, and then he finds a man sleeping near his home tree. He thinks the man might be a bandit on the run, so he calls him Bando. The man in turn calls Sam Thoreau. It turns out that Bando is really a college English professor who had gotten lost on the mountain. When he learns what Sam is doing, Bando honors and validates the boy’s self-imposed retreat from the city to the woods by naming him after American author and naturalist Henry David Thoreau (1817-1862). Thoreau lived in the woods next to Walden Pond in his hometown of Concord, Massachusetts, from 1845-1847, living a life of deliberate simplicity and honing his skills as a creative writer. But really, Sam’s attention to woodsmanship and methods of simplification outdo what Thoreau had done at Walden. Thoreau walked back to town on a regular basis and even traveled to Maine during his time at the pond. And he didn’t have to make his own tools or clothing, either. Still, his book about the experience, Walden, continues to inspire people to be independent and to be thoughtful about the ways in which they live. It has also recently ignited the tiny house movement.

Bando visits Sam again in Chapter 18 ("In Which I Learn About Birds and People") and Chapter 21 ("In Which I Cooperate with the Ending"). Author Jean Craighead George wrote many books with natural settings. She loved animals and nature, and she had been a fan of Henry Thoreau.

The reason that Bando called Sam "Thoreau" is because Bando was an English teacher and he knew a lot about literature from the old days.  The name Thoreau refers to this guy called Henry David Thoreau.

That Thoreau thought that people should life more of simple lives.  He said that people were too obsessed with their material possessions.  To prove the point, he went and lived in a cabin in the woods for a while.  He wrote a book about it called Walden.

So Bando calls Sam that because Sam had more or less the same idea that Thoreau had.

Why does Bando call Sam Thoreau in My Side Of The Mountain?

There is some logic in Bando's choosing to name Sam Thoreau. Let us remember that Thoreau is an important figure in American Literary History, and he wrote a famous book, entitled Walden, which describes his decision to leave society and civilisation and live an isolated and secluded life in nature where he lives off of the labour of his own hands and eats on the whole only what he can grow or gather himself. Bando, as he comes to see how Sam is living his life and the parallels between his situation and that of Thoreau, therefore chooses a very apt name to describe the way that Sam has turned his back on civilisation and is dependent on nature for all of his needs.

I have included a link below to the enotes study guide section on Thoreau's work so that you can gain more information about it should you wish. It is a really fascinating work and a key text in American Romanticism.