In the third verse of Haazinu, as a prologue to the poem, we read (Dvarim 32:3) “Ki Shem HaShem Ekra, Havu Godel L’Elokeinu”, “When I call out the Name of HaShem, give greatness to our God.”
This verse may sound familiar to you as it is the introductory verse of the Amida (Silent Devotion) in the Musaf (Additional Prayer said on holidays) and Mincha (Afternoon) services.
Rashi comments (Talmud, Brachot 21a) that when Moshe came to recite the poem, he said to B’nai Yisrael: “I will make a blessing first and then you will answer ‘amen.’”
Ki Shem HaShem Ekra, refers to the blessing and Havu Godel L’Elokeinu refers to the nation answering amen.
In the Mishna, Yoma 35b, we learn that during the Avoda, the Yom Kippur Service in the Beit HaMikdash (Temple), the Kohen Gadol (High Priest) states “Ana HaShem”, “I beg of You, HaShem” twice using the four letter Divine Name of the Tetragrammaton (Yud-Kei-Vav-Kei) followed by “Ki Vayom HaZeh Yichaper Aleichem Litaher Etchem Mikol Chatoteichem, Lifnei HaShem”, “For on this day He will make atonement for you, to cleanse you from all your sins, before HaShem.” The assemblage responds after each time that the Tetragrammaton is mentioned: “Baruch Shem Kevod Malchuto L’Olam VaEd”, “Blessed is the Name of the glory of His Kingship forever and ever.”
On Yom Kippur, “Baruch Shem…” is said in a loud voice to imitate the angels. The rest of the year, it is whispered (for example after we recite the first line of the Shma).
The Talmud, Yoma 37a explains the Biblical source:
It was taught in a Braita, Rebbi says “Ki Shem HaShem Ekra, Havu Godel L’Elokeinu”, Moshe said: At the moment that I mention the Name of God, you shall accord Him greatness.” The words are based on a verse from Nechemia 9:5 which were sung in a response format by the Leviim and answered by the congregation: “Kumu Barchu et HaShem Elokeichem Min HaOlam ad HaOlam V’Yivrechu Shem Kvodecha U’Meromam al Kol Bracha V’Tehila”, “…Rise up and bless HaShem forever and ever and let them bless Your glorious Name which is above every blessing and praise.”
According to Tosefta, Brachot, Chapter 6 and Brachot 63a, we learn from the above verse from Nechemia that the response for every blessing in the Beit HaMikdash was “Baruch Shem Kevod Malchuto L’Olam VaEd.”
The Braita teaches that when a blessing is recited (as in the repetition of the Shmoneh Esrei) after God’s name is mentioned (Barauch Atah HaShem), the congregation responds “Baruch Hu U’varuch Shemo”, “Blessed is He and Blessed is His Name.”
We learn from here that prayer is an active, responsive experience. The congregation focuses better when they know that they are not just there to listen to the service but they must actively respond and give God’s Name the honor that it deserves whether it is on a weekday or on Yom Kippur, the holiest day on the Jewish calendar.