or in the North of
Ireland, more like Tayg. But most English speakers are only familiar with the teeg pronounciation associated with the surnames
Teague or MacTeague, or
Teagan and Deegan (which can have other origins than
Tadhg).
In Scotland, incidentally, the name is spelt Taog and apparently pronounced tuk' by Gaelic speakers. Now there's a splendid name.
;)