"After initiation, the disciple's name must be changed to indicate that he is a servant of Lord Visnu. The disciple should also immediately begin marking his body with tilaka (urdhva-pundra), especially his forehead. These are spiritual marks, symptoms of a perfect Vaisnava." This is a verse from the Padma Purana, Uttara-khanda."
Caitanya-caritamrta, Madyam lila 1:208
"In the Padma Purana there is a statement describing how a Vaisnava should decorate his body with tilaka and beads: "Persons who put tulasi beads on the neck, who mark twelve places of their bodies as Visnu temples with Visnu's symbolic representations [the four items held in the four hands of Lord Visnu--conch, mace, disc and lotus], and who have visnu-tilaka on their foreheads, are to be understood as the devotees of Lord Visnu in this world. Their presence makes the world purified, and anywhere they remain, they make that place as good as Vaikuntha."
A similar statement is in the Skanda Purana, which says, "Persons who are decorated with tilaka or gopi-candana [a kind of clay resembling fuller's earth which is produced in certain quarters of Vrndavana], and who mark their bodies all over with the holy names of the Lord, and on whose necks and breasts there are tulasi beads, are never approached by the Yamadutas."
Nectar of Devotion, Chapter 9
Different types of tilaka markings denote the different sects of Vaisnavism, namely the impersonalists and the personalists. Gaudiya Vaisnava tilaka appears as two straight and perpendicular vertical lines on the forehead that meet between the eyes. Tilaka marks are ornamented in various ways. Sometimes white or yellow clay is used for marking the outer lines, and turmeric or red sricurna powder mark the central line. Curved tilaka is not to be worn Gaudiya Vaisnavas. Gaudiya Vaisnava tilaka is also known as udra pundra, or Visnu temple, which distinguishes the personalist Vaisnavas from the mayavadis, who use the three parallel lines, tripundra.
Members of the Kumara Sampradaya place on the forehead two vertical lines of white clay (gopichandana) with a central black spot. For members of the Laksmi Sampradaya, the representation of Namam on the Vaisnava's forehead is known as Thirumann, which means the sacred earth (dust). Namam consists of three vertical lines joined at the base, the two outer white lines signifying the worship of Brahama and Vishnu and the red centerline signifying the worship Mahalakshi. The Saivite tilaka has three pundra, or lines, on the forehead.
Bhaktivedanta Book Trust. HDG A.C. Bhaktivedanta Swami Srila Prabhupada.