The Story of Veronica's Veil is not found in the New Testament. It appears in early Christian history. This was not the real name of the woman alleged to have wiped Jesus' face, but rather a name ascribed to her. The name given was Veronica from the Latin Vera (true) and Icona (image) or Greek Eikon. Her name was Bernice in the Greek literature. Later legend says that Veronica brought the Veil to Rome where the Veil cured the Emperor Tiberius from an unknown malady. In addition, she is said to have given the veil to Pope Clement - the 4th Pope. However, other historical texts take the Veronica in a different direction, as we shall see. Veronica was also identified with the woman with the hemorrhage who touched the hem of Jesus' garment and was healed (Mark 5:29) of a 12 year problem of bleeding. Jesus stopped and asked who touched Him. He stated that power (dunamin in Greek) went out from Him and healed her. This woman healed by Jesus came to be identified in early Christian history as Veronica.
Readers of this site will know i have an interest in these legends as perhaps having a kernel of truth in them. It was interesting to read St. Irenaeus of Lyon, a Bishop living in what is now France, who was one of the great theologians of the second century. Fr. Heinrich Pfeiffer, a world renowned scholar of early Christian art, makes an interesting statement: "St. Irenaeus of Lyon (130-200) recounts in his work ‘Against Heresies’ that the followers of the Egyptian Gnostic heretic Carpocrates (2nd century), possessed and venerated images of Christ '...some are painted images, others made of other materials and are made according to the model executed by Pontius Pilate 'during the time in which Jesus was among men.'" [Francesco Barbesino, Cristianita n. 311 (2002) The Holy Face of Manoppello].
Research i am working on now looks at these icons and images, and also the main players - all figures from the Crucifixion death and burial of Christ - which becomes the basis of the Holy Grail legends. When you match this with a tomb of Jesus in Septimania - the research seems pretty interesting, non?