Then he summoned his twelve disciples and gave them authority over unclean spirits to drive them out and to cure every disease and every illness. The names of the twelve apostles are these: first, Simon called Peter, and his brother Andrew; James, the son of Zebedee, and his brother John; Philip and Bartholomew, Thomas and Matthew the tax collector; James, the son of Alphaeus, and Thaddeus; Simon the Cananean, and Judas Iscariot who betrayed him. Jesus sent out these twelve after instructing them thus, "Do not go into pagan territory or enter a Samaritan town. Go rather to the lost sheep of the house of Israel. As you go, make this proclamation: 'The kingdom of heaven is at hand.' (Mt 10:1-7)
Jesus called the twelve disciples to him. They were his disciples even before they began their ministry. They were following him and were living with him and were going around with him. There seemed to have been a preparation period. How ling was this period is not known to us. Authority that was given to them was more of sharing his healing power and power over the evil. Their main work was to remove evil in whatever form.
The author gives a list of names of twelve. This only goes to confirm that all his disciples were not given the authority. It was given to specific person. They were persons with individual identity. The identity was so specific that it went so far as to o avoid any confusion. There could have been more disciples with same name so the author goes to say that one is a brother of so and so or son of so and so etc. Jesus calls individuals and not groups or families. These individuals have specific identity.
These twelve are given the area of their activity. They cannot choose their place of ministry. They are given work-area and they are even told where to go and where not to go. They are to proclaim that the kingdom of God is at hand. This is the beginning of their work. The work that is given to them will have time duration and it will proceed and continue.