The use of the word quiver for a case of arrows dates back to the 13 century.
[ETYMOLOGY: 13th Century: from Old French cuivre; related to Old English cocer, Old Saxon kokari, Old High German kohhari, Medieval Latin cucurum]
As the Battle of Agincourt was in the 15th century, it is more than possible that the English longbowmen's draw string bag was called a quiver. There are hundreds of sites found when using the words quiver and Agincourt in a search.
It may well have been called something else, but the idea is at least 5000 years old.
In 1991, the body of a 45 year old man was discovered on the present-day border between Italy and Austria and dated to be from 3,300 BC. He was dressed in a leather clothe, a waterproof cloak made of grasses and carried a framed backpack, a utility belt with tools, a quiver of 14 arrows, a knife made from flint and a copper axe. The axe caused much interest as it's age pre-dated the previous estimations of the development of smelting copper by 1000 years. His wooden arrows had flint arrowheads and the quiver included a flap to keep the feathers dry. His body and hair tissues were analyzed and found to contain high amounts of copper and arsenic, by-products of smelting copper ore. He carried arrows of two lengths and it was estimated that he may have traded one of his copper axes for some arrows during his travels.
https://en.wikipedia.org/wiki/Ötzi#Tools_and_equipment
