The name Anson has its origins in the Old English language and is derived from the name Ansund or Ansund, which itself comes from the Germanic root words "ans" meaning "half" and "gund" meaning "battle". This suggests that the name was originally used to refer to someone who was only partially involved in a battle or conflict.

One of the earliest recorded uses of the name Anson dates back to the 7th century AD, where it appears in the Anglo-Saxon Chronicle, an annual record of events in Anglo-Saxon England. The name was relatively common among the Anglo-Saxons and was later adopted by the Normans after the Norman Conquest of England in 1066.

The first recorded bearer of the name Anson of historical significance was Anson of Hexham, a 7th-century Northumbrian monk and hagiographer who wrote the life of St. Cuthbert, a renowned Anglo-Saxon saint. Another notable figure was Anson of Palermo, a 12th-century English crusader who participated in the Third Crusade and is mentioned in the chronicles of the time.

In the 13th century, Anson de Multon (c. 1225-1276) was a prominent English nobleman and landowner who served as Sheriff of Yorkshire and Northumberland. During the Wars of the Roses in the 15th century, Anson Woodville (c. 1438-1491) was a loyal supporter of the House of Lancaster and fought at the Battle of Towton in 1461.

One of the most famous bearers of the name was George Anson (1697-1762), a British admiral and nobleman who circumnavigated the globe and achieved significant victories against the Spanish during the War of Jenkins' Ear. His exploits were recorded in the bestselling "A Voyage Round the World" by Richard Walter.

Other notable figures throughout history include Anson Burlingame (1820-1870), an American diplomat who served as the United States Minister to China, and Anson Phelps Stokes (1838-1913), an American businessman and philanthropist who founded the Anson Phelps Stokes Institute for Higher Education in New York City.