For everyone confused by the whole federation thing, trying to compare it to Twitter... Forget Twitter. Think e-mail. You can choose between different e-mail providers on different domains or even host your own server instance. Then you can communicate across those instances with other users on them.
No, it doesn't make sense to "claim" your nickname everywhere. Yes, you should choose the server wisely because all your data reside on that server without an easy way to migrate them...