Time happened. The Western and the Eastern Roman Empire did not have these differences you're pointing to in 476 a.d. Comparing the Byzantine Empire of th 15th century with the WRE of the 5th century is rather silly. With such a long time span everything will change.

They LITTERALLY had NOTHING in common with the romans that I can think of.

Because you're likely comparing something like Gladiator-era Rome with maybe the Byzantine Empire you've met through games around the Crusades, right? At a glance, they appear unrelated, but that comparison isn't very helpful. There's a thousand years between 100 and 1100 AD and a thousand and more reasons why things ended up the way they did.

If you went back to 1015, you'd find the predecessors of modern France, England, or Germany almost unrecognizable. And yet the average person will probably still see that history as part of their cultural heritage. So would a medieval Roman.

The Byzantine empire (Eastern Roman empire) was heavily influenced by their regional cultures, which were Greek and cultures of Anatolia. Greeks composed much of the civil servants, whereas in the Western Roman empire it remained controlled by the old Roman culture (but also the "barbaric" usurpers).

Because it wasn't. The people of the Byzantine Empire were Romans in name-only. They had little to no connection to the Itallic peoples who founded the Empire.