אלקי אבתיכם אלקי ‘ה ישראל בני אל תאמר כה” זה אלכים שלחני יעקב ואלקי יצחק אלקי אברהם (טו ג) “דר לדר זכרי וזה לעלם שמי
Regarding the passuk “zeh Shemi l’olam” Chazal explain (Pesachim 50a) that we have to read the word לעלם written without the vav, as if it says “l’alem” – from the term ha’alamah. In other words, we have to hide the Shem Hameyuchad – Shem Havaya”h, and not read it as it’s written in the Torah, but rather “vezeh zichri ledor vador” – it should be pronounced א-ד-נ-י.
The holy Zohar explains that these Names are the lofty sod, the secret, of the virtue of answering amen, because amen is numerically equivalent to 91, which is the same as the numerical value of the Shem Hameyuchad as it is written [ה“הוי] and as it is written [א.ד.נ.י.] and together they amount to 91.
Based on this, the Rokeach explains the words of the Breisa (Brachos 53a), that “the one who answers amen is greater than the mevarech.” It would seem that the mevarech is the one who praises and thanks Hashem, while the oneh merely agrees with his words. Why, if so, do Chazal say that the oneh amen is greater than the mevarech?
Because while the mevarech only mentions the Name of Adnus, the oneh amen after him mentions with his answer the Names of Hava”yah and Adnus together, and therefore, he is greater than the mevarech. (Haroke’ach, Hilchos Seudah 330; Ba’al Haturim Devarim 27:26)
Regarding the sod of answering amen and the sod of the Holy Names that are included in it, the mekubal Rav Aharon Hazaken of Kardina author of sefer Karnayim, describes it remarkably, and writes in Iggeres Hata’amim: “Because all the Holy Names, as one, contain hidden segulos that are covered up by the word amen...of which the passuk says (Yeshayahu 26:2): ‘Vayavo goy tzaddik shomer emunim,’ and it means to say that just like the one who guards the treasury, who is deep inside the inner chambers, likewise, this pure and holy word has a sources that is more valuable than pearls...If so you, Ben Adam, should see how many remazim, secrets and razim are based on the precious foundations...and where is the place of amen? Kodesh kodashim.”
The ancient siddur Seder Nehora Hashalem brings in the name of the early sages that indeed, at the time of answering amen, one should have kavanah to combine the Names of Hava”yah and Adnus which are numerically equivalent to amen. And he adds that this is alluded to in the passuk we say each morning in Hodu (Divrei Hayamim I 16:36): “Vayomru kol ha’am amen vehallel l’Hashem” – the whole nation should be strict to answer amen. And what should they have in mind with it? “Vehallel l’Hashem,” meaning to combine the Name of Adnus that is numerically equivalent to hallel, - l’Hashem to the Name Havay”ah, and combined they are numerically equivalent to amen.
HaRokeach Hilchos Seudah 330; Iggeres Hate’amim [Mantua 5342] p. 12b; Seder Nehorah Hashalem beginning of Ch. 15 and in the Haga”h