According to Geoffrey of Monmouth's influential but largely fictional history Historia Regum Britanniae, the realm was named after the legendary king Locrinus, the oldest son of Brutus of Troy.
In his Historia, Geoffrey uses the word "Loegria" to describe a province containing most of England excluding Cornwall and possibly Northumberland, as in this example from section iv.20 (from the Penguin Classics translation by Lewis Thorpe): Parishes were apportioned off, Deira being placed under the Metropolitan of York, along with Albany, for the great River Humber divides these two from Loegria.
[1]It was described by Chrétien de Troyes as "The Land of Ogres" (l'Ogres) in his poem Perceval, the Story of the Grail.
In various French works, Logres appears as the name of the land or the capital city (otherwise Camelot), its inhabitants can be known as either Loegrwys or Lloegrwys.
In some medieval German works, Logres is the personal domain of Gawain, as established by Wolfram von Eschenbach.