In "Fiddler on the Roof", in the three times I've seen it on Broadway (and in the production of it I'm currently in now), it's been pronounced "TEV-yeh."
Love the name Tevye, and it's all because of Fiddler. A man continuously trying to do the right thing, quoting (often incorrectly) the "good book," admiring the scholars and talking/complaining to God as if God were his best friend. Very lovable main character of a very powerful show. I highly recommend seeing the show (especially if you plan on giving your child the name, because it is connected that much with the play), and it gives the name Tevye a very friendly connotation for the most part.