Tadhg is pronounced Ty-g like tiger without the g. If you want to name your son
Teague you should name him
Teague.
I don't think most Americans would have a clue how to pronounce the name
Tadhg, and it would be very unfair to a little boy to have to keep correcting people about his name. The Gaelic 'adh' diphthong pronounced as a y is not something Americans have a clue about,
and even scholars fight about that kind of thing.
Tadhg is going to be pronounced
Tad -hig more than Tyg.
For more info on the name
Tadhg go here
http://www.iol.ie/~tadhgs/nametadhg.htm