We would guess that it was named ScoreCenter to begin with because that's all it offered: scores. Now, the app is much more fully featured, so it gets to be SportsCenter without worry of sullying the name. Version 4.0 of the app brings a number of improvements beyond the name change. The app now includes Favorites, so you can easily get news and scores about your favorite teams; Clubhouses, which are centralized spots for each team in every league; and Inbox, which seems to be the archived version of Favorites.
Real-time content is also improved with ESPN Now, which mixes together real-time game updates and social media updates; and, Game Pages have been improved with easier sharing options and easier access to GameCast. There is also finally a Search feature for the app.
Unfortunately, this update has only been released on iOS so far. Android received a minor update, but that only brought the app to version 3.2.1. No word on when Android will see the version 4 update. *Update* The new version of the app is now available for both iOS and Android.