It can also be considered a cognate of Eve and Lyn - then of Hebrew origin. There is a possible relation with the Gaelic 'eiblin' ('pleasant') as well.
The medieval name seems to have been used only by women, but it gave rise to a surname that was turned into a masculine given name as early as the 17th century. Evelyn is today used primarily by women, but it was common enough as a boys' name just a generation ago.
An example of it as a surname is the gardener and diarist John Evelyn. Novelist Evelyn Waugh is a famous male bearer, and Pre-Raphaelite painter Evelyn De Morgan is a female bearer.
In the 20th century, Evelyn was most popular in the 1910s and 20s. Recently it has been resurging.