Tadgh
(Tadhg is the misspelling!) Pronounced TEE(gh), with the gh not silent, but more like in dough--soft, barely pronounced, but there. You DO NOT PRONOUNCE THE D OR THE G. Irish Gaelic is weird like that. I love it, it's the name of one of my future sons.
Tadhg is actually the correct modern spelling for the name. Tadg and Tadc are older forms of this Irish name. It means "poet," and it generally pronounced TYG (like the first syllable in 'tiger'), although it is anglicized Taig and Teague. Both of these anglicized forms have come to be derogatory words for Irish Catholics in Northern Ireland, based upon how common the name is/was. Another tidbit, is that in the Irish language, the name Tadhg was so common that it became a slang term for 'every man.'