'Kathleen' Isn't an Irish Name

Reading about smithereens (see next post below) motivated me to look up the source of my daughter's name, and to a surprise.

Though words/names spelled in English with an -een ending are typically Irish diminutives, I found that Kathleen, a very popular Irish name, is not. (In my semi-Irish family, we have three generations of Kathleens – my daughter, my sister, and my aunt).

However, Wikipedia says:

Kathleen is a given name, used in English and Irish-language communities. Sometimes spelled Cathleen, it is an Anglicized form of Caitlín, the Irish form of Cateline, which was the Old French form of Catherine. It ultimately derives from the Greek name Aikaterine, the meaning of which is highly debated 

Greek?