According to Burke's Extinct Peerages, the name Skeffington is quite old. It is derived from the village where the family lived, Skeffington in Leicestershire.
According to Burke, the fist Skeffington of note was Sir William Skeffington who was knighted by Henry VIII of England and sent to Ireland, eventually becoming Lord Deputy of Ireland. This Sir William, returning home from Ireland, settled in Staffordshire, in the village of Fisherwick. It is quite common in the old English peerage records to see that the Staffordshire Skeffingtons are identified as the Skeffingtons of Fisherwick, while the Leicestershire Skeffingtons are identified as the Skeffingtons of Skeffington.