More like “fediverse” instead of “social”. Facebook is also a “social”, but it does not communicate with other fediverse instances. The fact that you are federated and share content is what should be in the name.

And behold: many instances DO use fediverse over lemmy in their name.

But Lemmy is not perfectly compatible with Mastodon and kbin. At the time some of the instances were made, Lemmy could not even federate with Mastodon at all. So it makes sense that instaces explicitly picked a name with Lemmy in it.