Teutorix is a purported Celtic name meaning "ruler of the people".
It is the precise cognate of the Germanic name Theoderic, from teuto "people" and rix "king, ruler".

The existence of this name is uncertain. It has been postulated as being behind the Welsh Tudur

Tudur

Tudur is the Welsh form of the given name Theodoric.People called Tudur include:*Tewdrig, king of Glywysing *Tudur Hen , eponymous founder of the Tudor dynasty*Tudur ap Gwyn Hagr Tudur is the Welsh form of the given name Theodoric.People called Tudur include:*Tewdrig, king of Glywysing (fl. 6th...

, which might as well be a late adoption of the Germanic name.
It has been read into a Roman-era (3rd century) inscription, discovered in 1784 in Wiesbaden

Wiesbaden

Wiesbaden is a city in southwest Germany and the capital of the federal state of Hesse. It has about 275,400 inhabitants, plus approximately 10,000 United States citizens...

 (at the time known as Aquae Mattiacorum in Germania Superior

Germania Superior

Germania Superior , so called for the reason that it lay upstream of Germania Inferior, was a province of the Roman Empire. It comprised an area of western Switzerland, the French Jura and Alsace regions, and southwestern Germany...

), edited in Codex inscriptionum romanarum Danubii et Rheni as no. 684: , interpreted as In honorem domus divinae, Apolloni toutiorigi.
This has given rise to a supposed "Apollo Teutorix" in 19th-century literature.
Rhys (1892) opined that "the interest attached to the word Toutiorix is out of all proportion to its single occurrence".
Rhys surmises that the "historical Teuton" (viz. Theodoric the Great

Theodoric the Great

Theodoric the Great was king of the Ostrogoths , ruler of Italy , regent of the Visigoths , and a viceroy of the Eastern Roman Empire...

) bore a name of the Gaulish Apollo as adopted into early Germanic religion.