The thing I know and unsure that it will help on your question is following:
In the wild, tortoises do not live in herd/group together, they live in "loose colonies", i.e. they live a solitary life but their territories overlap, so they encounter each other often and go apart thereafter.
In captivity, it is said that it is good to have for example two tortoises together (same gender obviously for as much peace as possible), that way leaving together they know their own kind, they know that they are tortoises and exhibit better natural instinct and behaviour. Having said that, there are tortoises in captivity who live happily on their own. The good example I know of on this forum is Harry the male Hermann who is 50 years old.
Sabina