I'm open to correction on this one but, essentially:

Toirdhealbhach is the old spelling of his name, rendered in Roman script and with h replacing the "séimhiú" mark or dot above a consonant which shows lenition (changes the sound or eliminates it). In modern Irish it becomes Traolach. Turlough is a kind of intermediate form which retains some Gaelic character but is used in English. Still with me....? ;>)

Regards