Because the converts in the early Church came from pagan religions, they had been given pagan names by their parents at birth. Often they had been named after some pagan deity.
When they rejected their pagan religion and were reborn into the community of the Church, they rejected their old name and took on a new one that had a Christian quality to it. It was one more sign of starting life all over at their Baptism/Confirmation.
Since you were already given a Christian name at your Baptism, there is no need for you to take a new one. Some people, however, do take a second or Confirmation name to add to their baptismal name. It’s been a custom in the Church and is still allowed.
The names chosen by the newly converted pagans usually had great significance for them. Through the chosen names, they sought to express something of the inner self and/or what they hoped to become — the ideal or goal they set for themselves as persons. A Peter (“rock”), hoped to become courageous like the Apostle, or immovable in faith. An Agatha (Greek for “beautiful”), hoped to acquire inward, spiritual beauty or to become beautiful in the eyes of God. In much the same way, the name by which you wish to be called when you are sealed with the Spirit should have true significance for you.
Today, many choose their baptismal name. The Church suggests this since one’s baptismal name already has real significance and because this reaffirms the idea that Confirmation completes our Baptism.
Some choose a second name. You are free to do so. However, the name should be a Christian name of a saint or other Christian whose personal faith and spiritual qualities are those you admire and would like to imitate.