When three people eat together they are obligated in zimun: Leader: “Rabbosai mir vellen bentchen” Others: “Yehi shaym…” Leader: “N’voraych she’ochalnu mishelo” Others: “Boruch she’ochalnu mishelo uvtuvo choyinu” Leader: “Boruch she’ochalnu…” After this, the leader then separates the zimun from Birkas Hamazon by saying “Boruch hu uvoruch shemo”, then begins the first beracha. (ShA1 – MB2,4 – ShaT3)
When ten or more ate together they are obligated to add Hashem’s name into the zimun: The leader says “N’voraych Elokaynu…”. The others respond “Boruch Elokaynu…”. No one should say “laylokainu” with a lammed. (ShA1)
If the leader forgot to say “Elokaynu”, he goes back to say the zimun again with the Shem as long as they have not yet answered. If they did answer, the leader cannot go back. The most he can do is to repeat “Boruch Elokaynu…” after them. (ShA2 – MB10)
If everyone forgot to say “Elokaynu”, they are yotzay the zimun, b'dieved. (MB10)