The given name Graham has its origins in the ancient Brythonic Celtic language, spoken in what is now parts of Britain. It is derived from the elements "gra" meaning "gray" and "ham" meaning "homestead" or "settlement". The name likely emerged in the early medieval period, referring to someone who lived near a gray stone house or village.

One of the earliest known bearers of the name was Graham of Dalkeith, a Scottish nobleman who lived in the 12th century. He was a witness to several royal charters during the reign of King William the Lion of Scotland. The Clan Graham, an ancient Scottish clan, takes its name from this early Graham line.

In the 13th century, Sir John Graham was a prominent figure in the Wars of Scottish Independence, fighting alongside William Wallace and Robert the Bruce against English rule. He was instrumental in the victory at the Battle of Bannockburn in 1314 and was later made Lord Graham.

The name Graham gained wider recognition in the 15th century with the rise of the House of Graham, a powerful noble family in Scotland. Patrick Graham, 1st Lord Graham (c.1445-1513), was a trusted advisor to King James IV of Scotland and played a key role in the Scottish Renaissance.

A notable bearer of the name in later centuries was James Graham, 1st Marquess of Montrose (1612-1650), a Scottish nobleman and military leader who fought for the Royalist cause in the English Civil War. He was executed by the Covenanters in 1650 for his loyalty to King Charles I.

In the 18th century, John Graham of Claverhouse (1648-1689), better known as "Bonnie Dundee", was a Scottish soldier and professional officer who fought for the House of Stuart during the Jacobite risings. He was killed at the Battle of Killiecrankie in 1689, becoming a romantic figure in Scottish folklore.