Q. If I hear someone make a bracha, perhaps the chazan in shul, and he mispronounces Hashem’s Name as is unfortunately common, either by saying Adinoi or Adeenoi, instead of Ado-noi,

3) May one say Boruch Hu Uvoruch Shemo after the mispronounced Name?
4) Or is it perhaps forbidden to bless such a name?

A. Answering “Boruch Hu Uvoruch Shemo” after hearing Hashem’s name in a brocho is not mentioned in the Talmud, however, it became tradition in many communities, but not all. Therefore it is omitted when one is in the middle of a prayer he may not interrupt.
Horav Shlomo Miller Shlit”a pointed out, as an example, that those who follow Brisker minhogim do not answer that praise at all. As mentioned in prior question (808), after the fact one complies with a brocho that contains one of Hashem’s mispronounced names, therefore, one may also answer this corresponding praise.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a