Not all priests continue to use their original baptismal names after ordination. Some orders do change their names, retaining their baptismal names as their legal names, and their religious names to signify the change they have made in their lives. This is usually not the case for "secular" (diocesan/parish) priests who retain their baptismal names and are then known as Father Lastname, Father Firstname, or Father Firstname Lastname.
Some orders may use a combination of baptismal name plus new religious name and thus become Father Harold Xavier Jones, or Father Ronald Ignatius Loyola Henderson.