The name Teague is an anglicized form of the Irish Gaelic name Tadhg, which originated in Ireland during the early medieval period. Tadhg is derived from the Old Irish word "tadg," meaning "poet" or "philosopher." The name was popular among the ancient Celts who highly valued poetry, storytelling, and wisdom.

One of the earliest recorded mentions of the name Tadhg can be found in the Annals of Ulster, a chronicle of medieval Irish history. The Annals mention a Tadhg mac Muireadhaigh, who was the King of Connacht in the 8th century AD.

In the 12th century, the name Tadhg gained prominence with the rise of the O'Toole (Ó Tuathail) and O'Daly (Ó Dálaigh) families, who were renowned for their poets and scholars. One of the most famous bearers of the name was Tadhg Og Ó Huiginn (c. 1550-1616), a celebrated Irish poet and historian.

As the name Tadhg spread beyond Ireland, it was anglicized to various spellings, including Teague, Tague, and Teige. One of the earliest recorded instances of the anglicized spelling "Teague" can be found in the writings of the English satirist Jonathan Swift (1667-1745), who used the name as a derogatory term for Irish Catholics.

Despite this negative association, the name Teague has been borne by several notable individuals throughout history. One of the earliest was Teague O'Regan (c. 1615-1666), an Irish Franciscan friar and historian who wrote extensively about the Irish Confederate Wars.

Other notable bearers of the name include Teague Lysaght (c. 1670-1723), an Irish Jacobite soldier and landowner, and Teague O'Brien (1718-1798), an Irish-born American soldier who fought in the American Revolutionary War.

In the 19th century, Teague Barry (1810-1870) was an Irish-born American businessman and politician who served as the Mayor of Chicago from 1857 to 1858.

Teague Galen (1867-1946), an American politician and lawyer, served as the 27th Lieutenant Governor of Idaho from 1923 to 1927.

While the name Teague has Irish roots, it has been adopted by various cultures and communities around the world, reflecting the enduring legacy of the ancient Celts and their rich linguistic and cultural traditions.