There's an amora (or at least one) in the Bavli named שימי. I think I've always heard this pronounced with an initial letter sin. However, I saw recently that the Koren-Steinsaltz edition has a initial shin. What support is there for either?
Jastrow identifies him as Shimi:
שִׁימִי pr. n. m. Shimi, name of several Amoraim. Men. 29ᵃ, a. fr. ש׳ בר חייא. Ib. ש׳ את art thou Shimi (and askest such a question)?; ib. 110ᵃ. Tem. 28ᵃ ש׳ בר אשי; a. e.
However, Wikipedia calls him Simi.
Who's Who in the Talmud only contains Shimi and no Simi.
Interestingly, it is difficult to tell how Rav Kanievsky pronounces it here (9:25).