The "what was spoken by the prophets might be fulfilled" in the above quote from Matthew is believed by some to be a reference to Isaiah 11:1, "There shall come forth a shoot from the stump of Jesse, and a branch shall grow out of his roots."
The original Hebrew word, pronounced nay-tser, translated into English as shoot, literally means a sprout, or branch, and figuratively a descendant. The name Nazareth is thought to be derived from the same original word, which would indicate that God either named the city Himself, or chose it to be the home town of the Messiah because of its name.
Jesus Christ was often referred to as a Nazarene, or Jesus of Nazareth, in both a complimentary way, by Himself and those who believed in Him, and in a derogatory manner, by those who didn't.
"And when He entered Jerusalem, all the city was stirred, saying, "Who is this?" And the crowds said, "This is the prophet Jesus from Nazareth of Galilee." (Matthew 21:10-11 RSV)
"Concerning Jesus of Nazareth, Who was a prophet mighty in deed and word before God and all the people" (Luke 24:19 RSV)
"But Peter said, "I have no silver and gold, but I give you what I have; in the name of Jesus Christ of Nazareth, walk." And he took him by the right hand and raised him up; and immediately his feet and ankles were made strong." (Acts 3:6-7 RSV)
"And as Peter was below in the courtyard, one of the maids of the high priest [see Caiaphas] came; and seeing Peter warming himself, she looked at him, and said, "You also were with the Nazarene, Jesus." (Mark 14:66-67 RSV)
"For we have found this man a pestilent fellow, an agitator among all the Jews throughout the world, and a ringleader of the sect of the Nazarenes." (Acts 24:5 RSV)
Fact Finder: (a) Is Christianity also called "The Way"? (b) Why?
(a) Acts 19:23 (b) John 14:5-6
See also The Way