Céilidh is the older spelling. Scottish Gaelic has dropped the use of acute accents, although they are useful guides to pronunciation, retaining only the grave accents. So Ceilidh would be correct in modern Scottish Gaelic orthography. Modern Irish spelling has dropped the 'dh' and therefore an accent has to be added to the i to indicate the correct sound; Céilí. A similar example would be the word for night, oidhche in Scottish Gaelic and older Irish spelling, oíche in modern Irish spelling.

I am not familiar with Ceilidh as a name, either in Scotland or Ireland, and I don't know if there is a connection between this word and the name Kayleigh (apart from the similar sound). Ceiliidh can mean a dance, a social evening with songs and story-telling, or simply a social visit to someone's house.