A coat of arms is a "personal" thing.There is not one symbol for the entire MOTES family.Assuming (and that's a big assumption) that there was once a knighted MOTES (I personally have not found one), his coat of arms would have been passed down to his eldest son - only.Additional sons could design their own, adding to the original, but only the eldest could officially wear that of his father.
In England a few years ago I got to meet a Scotish cousin (very, very, very distant) who had been knighted by Queen Elizabeth.When I asked about his coat of arms, he said he had never bothered.It's frightfully expensive; and since he only had daughters, the symbol would die with him.
I have searched many of the heraldy books, and I have never come across an official MOTES coat of arms.Of course, if you want to buy one of those generic ones (with the Motes name written at the bottom), I'm sure there are numerous sites on the internet that will be more than happy to take your money.
My father-in-law once purchased one of those books from Bath, OH - the ones that list "All the Motes since the Civil War."It came complete with a "history of the name" (great little piece of fiction - and almost exactly like the NORWOOD history), a"Motes Coat of Arms" (looked a lot like several I've seen), and a listing of names and addresses.My husband was listed in the book five times; he was in the Army and moved more frequently than most.(In one case the post office had changed our address from 66 S. Clear Creek Road to 33 S. Clear Creek Road - the decided the numbering should come from the other direction.We had never actually lived at either location at that time, but both were in the book!)