I have noticed that while making the Bracha for an aliyah, many people lift the Torah when Hashem's name is recited. Is there a source for this?
שערי אפרים 4:4 says to do so when saying "ונתן לנו את תורתו" and "אשר נתן לנו תורת אמת" in the blessings. I'm guessing people got confused.
It is just a nice minhag, and not Halacha. The lifting is done when we mention the Tora, not when Hashem's name is recited. It is to indicate that this is the Tora we are talking about (and no other).