ThaThe Babylonian Talmud has both Aramaic and Hebrew in it. In the handwritten versions which I reviewed, the 4 letter name of hashem is replaced with the yod-yod.
You can see this in the quotes from the bible used on Tractate B'rachot, 6A. The printed version I have replaces the 4 letter name with the Hey-apostrophe.
From the Munich Codex of 1342
6th line up from the bottom of the thinner lines next to the punch-out quote, second to last word.
9th line down, second to last word.