Rav Melamed in Peninei Halacha - Brachos says that at a communal shabbos meal, a zimun with Hashems name (10 people) is required, even if there are many seperate tables. This is because everyone started their meal at the same time and there is a sense of hitchabrut.
I was in Uman for Rosh Hashana with a few friends from America, and we slept, davened, and ate with a a certain sect of around 300 breslover chasidim from Beit Shemesh, in their compound.
After mussaf on day two, most of the chevre went to eat lunch in the cafeteria, while around 20 of us - 11 chasidim and my group of friends, stayed to daven mincha. We then went to eat.
In the cafeteria, there were 6 very long tables - my 8 friends and I picked a spot at one of the tables. Now, while some of us know many of the chasidim from years of being together in Uman and from visiting their beis medrash in beit shemesh, we ate all of our meals in the same spot in the cafeteria, us 9. There is an inherent disconnect, as they speak Yiddish (and a little bit of Hebrew) and we speak English (and a little bit of Hebrew). When there are speeches during the meal, we dont understand or pay attention. We dont know most of the songs. And most importantly, neither we or most of the chasidim wait until the end of the meal to bentch. In fact, im not even sure if there is a communal zimun at the end, as most of the chasidim just bentch with whoever they are eating with at their spot, when they finish.
So to wrap up, on the one hand, we are all eating together, and on the other hand, the 9 of us are eating seperately from the rest.
My question is: Were we allowed to include one of the chasidim who was sitting near us at the same table to be a tenth, and make a zimun with Hashems name?
גמר חתימה טובה
In your specific question of having another person who ate at the same table with you to join in your "zimun", you surely could have him join. Best would have been to have him eat something together with you and then it would be an absolute obligation. Breaking the social barrier with this "loner" sitting at your table has not only Halachic consequences as far as the zimun, but also you would have contributed to aspect of "achavah" of brotherly togetherness which is very important.
However, in the case of eating together in Uman, I am not saying that this is the Halacha , but it could be that he would join the zimun even if he had sat at another table. This is because from what I have been told from people who have been to Uman, is that each person belongs to a particular group who Daven and eat together at the same time .
If that is indeed the case, it would be like many people who eat in Yeshiva together who all eat the same food from the same kitchen at the same time. Although people sit at different tables, their intent is to eat together and they could do zimun . The language barrier is insignificant, especially in a case when you do know the people. It would NOT be like eating at a hotel, where although people may come to eat at the same time, they have nothing to do with each other.
Furthermore, if the people in the cafeteria are all served by the same people, this is an additional factor which can combine the people for zimun even if they are at different tables.
(see שו"ע או"ח סי' קצג, סי' קצה, קצו ופסקי תשובות שם. 'Peninei Halacha Berachot 5:2 )
All the best and גמר חתימה טובה