The name Caitlin was first recorded in the Social Security Name Database in 1955 when it was given to 5 girls. It's possible that it was pronounced like Kate-lyn, or that is was pronounced in its original Irish form (cot-leen); we don't know because the SSA does not record diacritical marks. FUN FACT: the name Kathleen is actually an anglicization of the Irish form, which is spelled Caitlín. Caitlín (sometimes found Caitilín) is the Irish Gaelic form of Cateline, a medieval French form of Catherine, which was brought to Ireland by the Normans in the 12th century. Catherine ultimately comes from the Greek Aikaterine, which has an uncertain origin. It was the name of a 3rd century saint, with who the name became associated. Because of this saintly association, the name was connected to Greek katharos, meaning "pure," and today most baby name books list it as meaning "pure," when it probably has no etymological connection to that root. It may derive from aikia meaning "torture," or could derive from the Greek goddess name Hecate.
Caitlin didn't become popular in the USA until the 1980s, peaking in 1988. In this time, a bunch of other spellings came into vogue, some of them surpassing the original in popularity. In 2021 (the most recent year for which we have data at this posting), the most common spelling was Kaitlyn, followed by Katelyn, Caitlyn, and Katelynn, with Caitlin being the 5th most popular spelling.
Note: I have included the -land, -lynd, -lind spellings because the Kateland I met pronounced it like Kaitlin. Some may actually pronounce the -d on the end, but based on other people I have met of the same generation with -land names (Ashland, Ryland), the final "d" is often silent.