Is there a Chinese name for the initiality theorem? This is a very specialized question.  There is a branch of mathematical logic called Homotopy Type Theory in English, and in Chinese 同伦类型论.  There is a Baidu page on it baike.baidu.com/item/同伦类型论.   A big current question in this field is in English the "initiality theorem."  In fact "initial" here is related to the idea of an initial object in category theory, and initial object in Chinese is often  初始对象.   But initiality theorem certainly cannot be expressed as  初始 定理 since that already means other things. I tried searching  同伦类型论 with initiality theorem and got no hits at all.

Can anyone tell me if there is a current standard Chinese name for this initiality theorem?

This kind of "initiality" is sometimes expressed as 初始性质 and that may be the closest i will get.  As I said, this is a very specialized question.  There may just not be any standard Chinese name for this theorem yet.
There is currently no standard name for this theorem in Chinese.