I think if I saw the name Taya written down, I would hesitantly pronounce it to rhyme with layer, but wouldn't be 100% certain that it shouldn't rhyme with higher. Like the Maya/Maya confusion, basically, although the other way round me for me: I assume Maya should rhyme with higher, but a lot of people default to it rhyming with layer. I can see this always being a bit of an issue with Taya. (Btw, before anyone complains, I'm aware this rhyming comparison only really works for English accents, but I'm tired and don't currently have the mental capacity to think up words that rhyme in Scottish/American/Canadian etc accents, sorry. OP seems to have a non-rhotic accent anyway.)
I prefer Talia or Rhea, which have some similar sounds but feel more established and classic. I also like Téa, but people miss off accents in this country quite a bit, and you couldn't be sure she wouldn't be called "tea" occasionally... 
To pps, Thea is Greek in origin, and pronounced a bit like Thaya (Greek and English both have the "th" sound). I quite like the French pronunciation, though, but think if you're in the UK, people will default to the British version.