“Son of David” was a very well know title for Jesus among the Jewish people of his day. Matthew was written to Jewish people so, we would expect it to be used their since it meant one in the lineage of the messiah.
The Genealogy of Jesus ] A record of the genealogy of Jesus Christ the son of David, the son of Abraham:
But after he had considered this, an angel of the Lord appeared to him in a dream and said, "Joseph son of David, do not be afraid to take Mary home as your wife, because what is conceived in her is from the Holy Spirit.
Jesus Heals the Blind and Mute ] As Jesus went on from there, two blind men followed him, calling out, “Have mercy on us, Son of David!”
All the people were astonished and said, “Could this be the Son of David?”
A Canaanite woman from that vicinity came to him, crying out, “Lord, Son of David, have mercy on me! My daughter is suffering terribly from demon-possession.”
Two blind men were sitting by the roadside, and when they heard that Jesus was going by, they shouted, “Lord, Son of David, have mercy on us!”
The crowd rebuked them and told them to be quiet, but they shouted all the louder, “Lord, Son of David, have mercy on us!”
The crowds that went ahead of him and those that followed shouted, “Hosanna to the Son of David!” “Blessed is he who comes in the name of the Lord!” “Hosanna in the highest!”
But when the chief priests and the teachers of the law saw the wonderful things he did and the children shouting in the temple area, “Hosanna to the Son of David,” they were indignant.
"What do you think about the Christ ? Whose son is he?" “The son of David,” they replied.
When he heard that it was Jesus of Nazareth, he began to shout, “Jesus, Son of David, have mercy on me!”
Many rebuked him and told him to be quiet, but he shouted all the more, “Son of David, have mercy on me!”
Whose Son Is the Christ ] While Jesus was teaching in the temple courts, he asked, "How is it that the teachers of the law say that the Christ is the son of David?
the son of David, the son of Jesse, the son of Obed, the son of Boaz, the son of Salmon, the son of Nahshon,
He called out, “Jesus, Son of David, have mercy on me!”
Those who led the way rebuked him and told him to be quiet, but he shouted all the more, “Son of David, have mercy on me!”
Whose Son Is the Christ? ] Then Jesus said to them, "How is it that they say the Christ is the Son of David?
Those who asked is this not the carpenters’ son were unbelievers, in fact due to their lack of faith, Jesus was unable to do many miracles in their area.