I’m going to be reading lines from “The Bacchae” this evening, and I’m a little worried about some of the character names- the umlauts (two little dots above the letter?) really throw me off.
Teiresias- I’ve been saying it as ‘Ty-REE-see-us’ is this correct? 
Agaue- (has an umlaut above the final ‘e’. How the hell do you pronounce this one? Agow? Agua? Agwee?
Autonoe- (Also has an umlaut above the final ‘e’ ) ‘Auto-nowie’? ‘Out-o-no’?
Someone more knowledgable about these particular names will be along shortly, I’m sure, but I can tell you that the two dots (here known as a diaeresis) indicate that the two vowels are to be pronounced separately (as in naïve).
So my educated guess on the last two names would be Ah-GOW-ee (as in COW) and Aw-TAHN-oh-ee (like autonomy without the m).
I am perfectly willing to be corrected on either of these guesses.
Scarlett67 is right.
To me, Ty ree see us is fine, but you could get away with Tay ree see us as well.
Autonoe- the original may have sounded a little more like aw tahn uh eh, but modern English does not really transliterate exactly from greek. Either "eh " or “ee” would pass, the long e being the more common English pronunciation of the name.
If you want to pretend to be a modern Greek speaker, you could change that “aw” sound to an “av” sound, and the final letter to an “ee”. Av tahn uh ee. And demotic Greek speakers would be impressed, everyone else would want to know what the hell you were reading.
The nice thing about ancient Greek is we don’t really know exactly how they pronounced things - we know they had tonal inflections (like Chinese) that would make it seem sing-song to us, and modern Greek pronunciation has simplified the pronunciation - i, oi, eta, (short “e”), y and u are all usually pronounced like a long e “ee.” I remember being told in college that modern English speakers have accepted name pronunciations that were actually the common mispronounciatons of school boys in the 17th and 18th centuries. To switch to Latin, what was probably Cay -saar we pronounce as See-sar.