Empire!

[beale]

What was the Roman Empire called after it uprooted to Constantinople?

[jake-the-peg]

The Byzantine Empire?

http://www.metmuseum.org/explore/Byzantium/time.html

[Grunty]

It was first calloed the Eastern Roman Empire, then as Jake says, it adopted the name Byzantium.  This is a useful site:

http://www.stormfront.org/whitehistory/hwr20.htm