I think this will emerge over time. But it seems from the software design that the intention is for people to identify to a substantial extent with the server. First because there is the Local feed (which on many servers is a fire hose, although not as much as the Federated feed, which I suspect will disappear as it's unusable and possibly a resource hog), and second because if you display your followers, those who are on the local server have the server name removed (e.g., if you are on xyz.social I will appear as "@sTeamTraen@mastodon.social", whereas if you are also on mastodon.social then I will just appear as "@sTeamTraen").
Basically I think Mastodon is a fabulous idea for a world where there is also Twitter, but any large-scale migration from Twitter will mess it up very badly. The key point is that it's decentralised, and Twitter isn't, and most of the issues will emerge from there: "My Mastodon post was deleted", no, your xyz.social post was deleted, and you need to understand that.