If ten or more men ate together, then they recite the Zimun with the word "Elokenu." The leader announces, "Nebarech Elokenu She’achalnu Mi’shelo," to which the others respond, "Baruch Elokenu She’achalnu Mi’shelo…" which he then repeats.
If the group realizes after completing the Zimun that they had forgotten to include the word "Elokenu," and had recited the Zimun as though there wasn’t a Minyan present, they do not repeat the Zimun. Even if they realized their mistake before they began reciting Birkat Ha’mazon, they do not repeat the Zimun. A Minyan fulfills its obligation of Zimun even without reciting "Elokenu," and Zimun should not be recited twice. As such, even if they forgot to include "Elokenu," they should not repeat the Zimun. This is the ruling of the Shulhan Aruch (Orah Haim 192:2), based on the Orhot Haim (Rav Aharon Ha’kohen of Lunel, Provence, late 13th-early 14th century).
This applies even if the leader of the Zimun realized the mistake before he repeats "Baruch Elokenu She’achalnu Mi’shelo." Once the rest of the group recited "Baruch She’achalnu Mi’shelo," he must repeat their recitation, without "Elokenu," since the Zimun had already been established as a Zimun without God’s Name. This is the ruling of the Hid"a (Rav Haim Yosef David Azulai, 1724-1806), in his work Shiyureh Beracha (192).
If, however, the leader realized his mistake after his initial announcement of "Nebarech She’achalnu Mi’shelo," before the rest of the Minyan recited "Baruch She’achalnu Mi’shelo," then he may correct his mistake and recite "Nebarech Elokenu She’achalnu Mi’shelo." As long as the rest of the group had not yet recited "Baruch She’achalnu Mi’shelo" without "Elokenu," he may correct his mistake to include "Elokenu." By the same token, if he mistakenly omitted "Elokenu" when he introduced the Zimun, and recited "Nebarech She’achalnu Mi’shelo," but the group realized his mistake and they recited the proper text of "Baruch Elokenu She’achalnu Mi’shelo," he may then follow suit and repeat "Baruch Elokenu She’achalnu Mi’shelo." Since the group recited the correct text, with "Elokenu," the leader may also include "Elokenu" in his repetition. This is the ruling of several authorities, including the Ben Ish Hai (Shana Rishona – Korah 2) and the Kaf Ha’haim (192:16).
(Based on Rabbi Moshe Halevi’s work Birkat Hashem, vol. 2, p. 496)
Summary: If a Minyan that ate together mistakenly omitted "Elokenu" from the Zimun, they do not repeat the Zimun. If, however, the leader realizes his mistake immediately after his announcement of "Nebarech She’achalnu Mi’shelo," he may correct himself and recite the proper text of "Nebarech Elokenu She’achalnu Mi’shelo." If he did not correct his mistake, but the others realized the mistake and they responded with the correct text, with "Elokenu," then the leader, too, recites "Elokenu" when he repeats their response of "Baruch Elokenu…"
