Aaryn is a modern spelling of Aaron or Erin, most often tied to the Hebrew name Aaron of uncertain ancient meaning.
Aaryn is a phonetic reimagining of Aaron, the ancient Hebrew name borne by Moses's brother and the first High Priest of Israel. The original Aharon is of uncertain etymology — scholars have proposed derivations from the Egyptian aha rw (warrior lion), from the Hebrew har (mountain), and from various other roots, leaving the name with a pleasingly mysterious linguistic prehistory. Whatever its ultimate source, Aaron entered the Christian and Jewish traditions as a name of priestly dignity and brotherly loyalty, and it has never entirely left.
The spelling Aaryn — with its doubled A and the y substituting for the terminal on — belongs to the late twentieth century's creative approach to traditional names, particularly in American naming culture, where spelling variation became a way of personalizing inheritance. It also creates a visual and phonetic softness that makes the name feel more gender-neutral than the conventional Aaron, and indeed Aaryn appears as both a masculine and feminine name in contemporary usage. There is something of the name Erin audible in it as well, the Irish Éire (Ireland) glimmering beneath the Hebrew structure.
Historically, Aaron has been carried by figures from Aaron Burr — Alexander Hamilton's fatal rival and America's third vice president — to Aaron Copland, whose music defined a certain vision of the American landscape in the twentieth century. Aaryn as a spelling variant is newer and less laden with specific historical association, which gives it a fresh-slate quality that some parents prefer: the ancient name's sound and spirit, worn lightly.