The name itself derives from the Irish Tiobraid Fhachtna, meaning the well of Fachtna, suggesting an early Christian or pre-Christian sacred site in the vicinity. Graveyards in such townlands frequently occupy ground that was considered significant long before any church was built there, the burial use simply continuing a habit of sanctity that had already taken root.

Tibberaghny was the site of an early ecclesiastical settlement, and the area retains traces of that long occupation in its placename and its graveyard. Early Irish graveyards of this type often cluster around the remains of a medieval parish church, itself built on or near the site of a much older foundation. The association with a named holy well, embedded in the townland's Irish form, places Tibberaghny within a wider pattern of early Christian settlement along the Suir valley, where monastic communities and their associated burial grounds shaped the local landscape in ways that persisted for centuries. The graveyard as it survives today represents a continuum of use that can stretch from early medieval times through to the post-Reformation period and beyond, the headstones of later centuries sometimes marking ground that was already ancient when they were set.