So it looks like my real name is Dunholme, Hill Island

The name "Durham" comes from the Old English "dun", meaning hill, and the Old Norse "holme", which translates to island

He is officially styled The Right Reverend Father in God, (Christian Name), by Divine Providence Lord Bishop of Durham, but this full title is rarely used. In signatures, the bishop's family name is replaced by Dunelm, from the Latin name for Durham (the Latinised form of Old English Dunholm). In the past, bishops of Durham varied their signatures between Dunelm and the French Duresm. Auckland Castle has been the official residence of the Bishops of Durham since 1832.

From this wikipedia article