The Registrar's Scroll is a spool of parchment that registers the name of all school-age children (presumbly those in the Midwestern wizarding territory). It is kept in the Registrar's Office of the Charmbridge Academy, and records the names sent to it by the Central Territorial Census Office in Chicago.
Thomas Bagby is the record-keeper in the department that transmits those names.
It is possible to alter the Scroll, as Charmbridge Dean Lilith Grimm did in 2007 when she used an editing ink charm to change the name of a student from her paternal birth name to show that of her mother's maiden name. The student in question managed to break into the Registrar's Office and cast an editing-ink-reversal-charm in order to determine her true identity and that of her father.