The name Elyssa is believed to have its origins in Greek culture and language. It is a variant of the Greek name Elissa, which itself is a shortened form of the name Elisabet, the Greek form of the Hebrew name Elizabeth. The name Elizabeth means "God is my oath" or "consecrated to God" in Hebrew.

Elyssa is thought to have first appeared in ancient Greece, where it was used as a feminine name. It likely emerged as a shortened version of Elissa, which was a popular name among the Greek population during that time period. The name may have been influenced by the Greek word "elisso," meaning "to wind" or "to twist," possibly referring to the twisting or winding nature of a river or stream.

One of the earliest recorded instances of the name Elyssa can be found in the works of the ancient Greek historian Herodotus, who lived in the 5th century BC. He mentioned a woman named Elyssa in his writings, though details about her are scarce.

In the Middle Ages, the name Elyssa saw some use among the Byzantine Greeks, though it was not as common as other Greek names at the time. One notable figure from this period was Elyssa of Constantinople, a Byzantine noblewoman who lived in the 10th century AD.

During the Renaissance, the name experienced a resurgence in popularity, particularly in Italy. One of the most famous individuals with the name Elyssa was Elyssa Baciocchi, an Italian noblewoman and sister-in-law of Napoleon Bonaparte, who lived from 1777 to 1820.

In more recent times, the name Elyssa has been used across various cultures and regions, though it remains relatively uncommon. Notable individuals with the name include Elyssa Jerret, an American actress born in 1982, and Elyssa Davalos, a Canadian actress born in 1992.

Another notable figure with the name Elyssa was Elyssa Bazadier, a French painter and sculptor who lived from 1692 to 1761. She was known for her realistic portraiture and was a member of the Royal Academy of Painting and Sculpture in France.