The Irish name of the bird whose call sounds like Cúcúc is
"Cuach"

Which has other meanings:

cuach [ainmfhocal baininscneach den dara díochlaonadh]
éan a deir cú-cú agus a bheireann ubh i nead éin eile.

cuach [ainmfhocal firinscneach den cheathrú díochlaonadh]
babhla; corn (óil).

cuach [ainmfhocal baininscneach den dara díochlaonadh]
ceirtlín, beart, ribín snaidhmthe go deas ar ghruaig.

Agus anois tá na focail seo ag rith trí mo cheann

http://celtic-lyrics.com/forum/index.php?autocom=tclc&code=lyrics&id=622

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Personally, I'd avoid Cúcúc as a name, because of the meaning in English, and other languages.

http://dictionary.reference.com/search?q=cuckold&x=31&y=11