The name Alyssa has its origins in the Greek language and is a feminine form of the name Alyssos, which was a masculine name derived from the word "alysso" meaning "to go mad" or "to be demented." The name was likely chosen in ancient times to ward off madness or mental illness.

In Greek mythology, Alyssa was the name of a Sicilian nymph who was transformed into a stream after refusing the advances of the god Vertumnus. This mythological figure is one of the earliest recorded instances of the name's use.

The name Alyssa gained popularity in the Middle Ages, particularly in France and Italy, where it was sometimes spelled as Alisia or Alycia. During this time, the name was often associated with nobility and was borne by several members of the aristocracy.

One of the earliest recorded individuals with the name Alyssa was Alyssa of Ferrara, an Italian noblewoman born in 1265 who served as a patron of the arts and supported the work of famous poets and artists of her time.

In the 16th century, Alyssa Pico della Mirandola (1508-1589), an Italian philosopher and writer, gained recognition for her work in promoting the education of women and challenging the traditional gender roles of her era.

During the Renaissance period, the name Alyssa was also borne by Alyssa Gonzaga (1549-1626), an Italian noble and patron of the arts who was known for her support of artists and intellectuals.

In the 19th century, Alyssa Browning (1838-1912), an American social reformer and activist, worked tirelessly for the advancement of women's rights and the abolition of slavery.

Another notable figure with the name Alyssa was Alyssa Toklas (1877-1967), an American writer and partner of the famous writer Gertrude Stein, who played a significant role in the Parisian art and literary scene of the early 20th century.