Names starting with Cai

Caitlín - Irish Gaelic form of Old French Cateline, meaning "pure."
Cailín - Irish Gaelic name meaning "girl."
Caitrín - Irish Gaelic form of French Catherine, meaning "pure."
Cainan -   Anglicized form of Hebrew Qeynan, meaning "possession." In the bible, this is the name of a son of Enosh. 
Cailte - Irish namemeaning "the thin man." This is the name of a character from the Fenian cycle.
Caileigh - Variant spelling of English Kayleigh, meaning "slender."
Cairo - American English name derived from the name of the Egyptian city of Cairo, from Arabic al-Qāhira, meaning "victorious." 
Caiside - Gaelic byname derived from the word cas meaning "curly(-headed.)" Cassidy is the Anglicized form.
Caitlyn - Anglicized form of Irish Gaelic Caitlín, meaning "pure."
Cai -   Variant spelling of Scandinavian Kai, possibly meaning "lord."
Cailean - Scottish Gaelic name meaning "whelp; young pup."
Cait - Short form of Irish Caitríona and Scottish Caitrìona, meaning "pure."
Caitriona - Scottish Gaelic form of French Catherine, meaning "pure."
Caitie - Pet form of Irish Caitríona, meaning "pure."
Caitria - Variant form of Irish Gaelic Caitrín, meaning "pure."
Cairbre - Irish Gaelic legend name of an Ulster warrior, meaning "charioteer."
Cairistine - Scottish Gaelic form of Latin Christina, meaning "believer" or "follower of Christ."
Caia - Danish variant spelling of Scandinavian Kaia, meaning "pure."
Cailyn - Anglicized form of Irish Cailín, meaning "girl."
Caius - Variant spelling of Roman Latin Gaius, meaning "lord."
Cainnech - Gaelic byname meaning "comely; finely made." Kenneth is an Anglicized form. 
Caïn - French form of Hebrew Qayin ("acquired, possessed") and Greek Kaïn ("maker; fabricator" i.e. "smith"). 
Cairistìona - Scottish Gaelic form of Latin Christiana, meaning "believer" or "follower of Christ."
Caitríona - Irish Gaelic form of French Catherine, meaning "pure."