"Grange" means farm. What is the significance of the man's name being "Granger" in Fahrenheit 451?
In Ray Bradbury's Fahrenheit 451, Granger's name comes from the root word "grange," yes, but a better correlation is the word "granderize," which means:
to illustrate (a book) by later insertion of material, esp. prints cut from other works.
According to my dictionary, the term is originally from "the late 19th cent.: from the name J. Granger (1723–76), English biographer."
So, it has to do with books, namely to later add or amend that which has already been written. As you know, Granger and his Book People memorize important books to preserve them. They, in effect, illustrate (or imprint) them in memory for recitation later.
To use your word "grange," here's its origins:
ORIGIN Middle English (in the sense [granary, barn] ): from Old French, from medieval Latin granica (villa) ‘grain house or farm,’ based on Latin granum ‘grain.’
So, Granger is one who stores books in his head the way that a barn or farm stores grain. Grain is often used a metaphor or as imagery for knowledge and time. He also does so in exile, out in the country away from the city, as the word denotes.
I do not disagree with the first answer, but I am assuming that your teacher gave you the question just the way you asked it and you are supposed to discuss the relation between the word "farm" and Granger's character.
To me, there are two connections.
Yes, a farm is a place to store grain. But it is also a place where new life grows. I think this is a clear connection. Granger and people like him are the hope for the future -- they are the people who have the chance to create new life (intellectually speaking) after the society is destroyed.
Second, I think that farms and rural areas are very much the opposite of what the dominant society is about. The society in this book is about fast cars and parlour walls and crowded cities where you are never alone. This is not what farm life is like.
So Granger's name indicates how different he is from modern society and how he will have a part in growing a new society.