Answer: Moshe Rabbeinu exclaimed, “When I call upon the name of Hashem, exalt our G-d.” Onkelos translates this verse to mean that Moshe Rabbeinu meant to say that when I mention Hashem’s name in prayer, give praise to Hashem our G-d. Based on this, the Tur (Chapter 124) writes that he heard his father, the great Rabbeinu Asher, recite “Baruch Hu U’Varuch Shemo” (“Blessed be He and blessed be His name”) on any blessing he would hear in order to fulfill the above verse which commands us to exalt and give praise to Hashem any time we hear His name recited in a blessing by reciting “Baruch Hu U’Varuch Shemo.” This is indeed our custom and anytime the Chazzan mentions Hashem’s name during the repetition of the Amida prayer or other blessings, we all reply by exclaiming, “Baruch Hu U’Varuch Shemo.” At the conclusion of the blessing, the congregation answers, “Amen.”
Maran Ha’Shulchan Aruch (Chapter 124) rules likewise: “Upon hearing any blessing in any place, one should exclaim, ‘Baruch Hu U’Varuch Shemo.’”
Nevertheless, since reciting “Baruch Hu U’Varuch Shemo” is not a complete obligation, when one is in the middle of reciting Pesukei De’Zimra, although one must answer “Amen” to blessings he hears at this time (since answering “Amen” is completely obligatory), one should not answer “Baruch Hu U’Varuch Shemo” so as not to interrupt one’s Pesukei De’Zimra with something not completely obligatory. Many Acharonim rule likewise. Indeed, Hagaon Harav Moshe Feinstein zt”l writes in his Responsa Igrot Moshe (Volume 2, Chapter 98) that since answering “Baruch Hu U’Varuch Shemo” is not a complete obligation, one should not interrupt while reciting Pesukei De’Zimra in order to say it. He adds that since it is not a complete obligation, people are not so meticulous to recite it every time they hear a blessing being recited; rather, people are only careful to say it upon hearing blessing recited among the congregation, such as the blessings of the Chazzan’s repetition of the Amida prayer. In any case, although it is preferable to answer “Baruch Hu U’Varuch Shemo” upon hearing any blessing being recited alone (without a Minyan) as well, one must, nevertheless, not interrupt one’s recitation of Pesukei De’Zimra by reciting “Baruch Hu U’Varuch Shemo.” Maran Rabbeinu Ovadia Yosef zt”l rules likewise in his Responsa Yabia Omer (Volume 2).
In the next Halacha we shall, G-d-willing, discuss whether “Baruch Hu U’Varuch Shemo” should be answered for every blessing one hears or if there are some blessings to which “Baruch Hu U’Varuch Shemo” should not be answered.