OK, so this is a greek name, and it is spelt Θάλεια inn greek. This translates directly to Thaleia, but regardless, it is definitively pronounced with a 'th' as confirmed by many, many greek speakers. If it was 'TAH-lee-yah' then it would be spelt Talia or Tahlia. To pronounce the name Thalia 'TAH-lee-yah' is incorrect. This is very much a pet peeve of mine.
This is a comment from the name website Behind The Name, from the user thalia33. I did not write it myself.
Being a Greek woman bearing the name Thalia myself, I can end the pronunciation debate. I can assure you one hundred percent that the name is pronounced "THAL-eeah" In Greek, the accent is placed on the first alpha meaning the emphasis should be heard when pronouncing that letter. Furthermore, the first letter in the name when it is spelled in Greek is theta, which ONLY makes the th sound. Although other cultures do use this name, it is of Greek origin and this is technically the one and only way to pronounce it although I suppose other cultures are welcome to modify it if they wish. I do have one request, PLEASE if you are planning on naming your daughter Talia do not spell it "Thalia". First of all th always makes the th sound in English (the h is NEVER silent!) and secondly, it just adds to the confusion about the pronunciation of the name. The Percy Jackson movie, for example, is completely wrong and it is agitating to see a supposedly Greek movie pronouncing the name wrong. You have no idea how irritating it was growing up as Thalia and consistently being called Talia to the point where it just might as well have been my name. It felt as though I was being stripped of my uniqueness (as Talia, although not a common name itself, is much more common than Thalia at the very least) and of my cultural background that I identified with. So please, whenever you see "Thalia" it is pronounced with the th sound, and Talia should ONLY be spelled just like it sounds. Thank you.― thalia33 17/Mar/2016