Coill an Chuilinn would be ‘the holly wood’, ‘the wood of the holly-tree’ (wood of some particular holly tree),
Coill Chuilinn, I believe, would be a general, indefinite, ‘a holly wood, a wood of holly’.
cuileann is ‘holly-tree’ in the nominative, if you want to use it as an attribute you need a genitive
cuilinn ‘holly’s, of a holly-tree’, and since it is a masculine noun, the definite genitive ‘of the holly’ is
an chuilinn.
There is a similar place name in Ireland:
Cill Chuilinn (anglicized as
Kilcullen), meaning ‘church of holly, holly church’.
EDIT: since FGB states that
cuileann might be feminine, something like
*coill na cuilinn (or: cuilinne?) might be ok in some dialects. Someone who knows a dialect that uses this word as a feminine one would need to confirm.