Clan Graham is a Scottish clan

Scottish clan

Scottish clans , give a sense of identity and shared descent to people in Scotland and to their relations throughout the world, with a formal structure of Clan Chiefs recognised by the court of the Lord Lyon, King of Arms which acts as an authority concerning matters of heraldry and Coat of Arms...

 who had territories in both the Scottish Highlands and Lowlands.
Legend has it that the first Graham was one Gramus who forced a breach in the Roman Antonine wall known as Graeme's Dyke in 420 A.D. However, historians generally believe that the Grahams were of Norman descent.

The surname Graham is derived from the English place-name Grantham

Grantham

Grantham is a market town within the South Kesteven district of Lincolnshire, England. It bestrides the East Coast Main Line railway , the historic A1 main north-south road, and the River Witham. Grantham is located approximately south of the city of Lincoln, and approximately east of Nottingham...

, Lincolnshire, which appears in the Domesday Book

Domesday Book

Domesday Book , now held at The National Archives, Kew, Richmond upon Thames in South West London, is the record of the great survey of much of England and parts of Wales completed in 1086...

 both as Grantham and Graham.