You are correct that taking a confirmation name is an act of personal piety and not part of the liturgical rubrics for confirmation. In theory one could change one’s confirmation name if one wishes. As a practical matter though, I do not recommend doing so. The saint chosen at confirmation is a special friend in heaven who has been praying faithfully for the individual and deserves to continue to be honored by the Catholic who chose that saint’s name at confirmation. Rather, I recommend adding the new saint’s name to the existing confirmation name to create a double name. For example, someone who chose the name Michael at confirmation for St. Michael the Archangel and who later developed an affinity for St. Philip Neri might change his confirmation name to Michael Philip. Such a change would not be officially recorded by the Church, but if asked the confirmation name, a person could give the new double name.