The name Terance is derived from the Latin name Tertius, which means "third" or "the third one". It is believed to have originated in ancient Rome during the Roman Empire era, around the 1st century AD.

The name Terance was initially used as a personal name, as well as a cognomen or family name among Roman families. It was often given to the third son born in a family, indicating their birth order. The spelling variations of the name during that time included Tertius, Tertullus, and Terrentius.

One of the earliest recorded references to the name Terance can be found in the works of the Roman playwright Terence (195-159 BC), whose full name was Publius Terentius Afer. He was a renowned author of comedies, and his plays were widely popular during his lifetime and for centuries after.

In the 4th century AD, the name Terance was also borne by a Christian martyr named Saint Terence, who was killed during the persecution of Christians under the Roman Emperor Decius in 250 AD. He is venerated as a saint in the Catholic Church.

During the Middle Ages, the name Terance continued to be used, particularly in areas that were part of the former Roman Empire. One notable figure from this period was Terance of Portugal (1391-1457), a Franciscan friar and missionary who worked in Africa and Asia.

In the Renaissance era, the name Terance was popularized by the English poet and playwright Terence Vere Taaffe (1548-1605), who was also known as Terence Vere. He was a prominent figure in the English literary circles of the Elizabethan era.

Another famous bearer of the name was the French philosopher and mathematician Terence Tao (born 1975), who is widely regarded as one of the greatest mathematicians of the 21st century and has made significant contributions to various fields, including harmonic analysis, combinatorics, and number theory.