Gailyn is a unique, modern name of American origin. It's an adaptation of Gale, which means 'storm' or 'jubilee'. The 'lyn' ending gives it a distinct, feminine touch. Gailyn gained popularity in the United States during the late 20th century and has since been used occasionally.
"Gailyn saw its peak popularity during the mid-20th century, with 11 births recorded in 1952. However, it was quite uncommon for most of the 1990s, as only one birth was registered in 1993."