Actually, those don't seem quite right. I would go with these Swedish names:
Albania > Albanien
Armenia Minor > Armenia Minor (Latin, thus good everywhere)
Byzantine > Bysans, or the Latin Byzantium
Duchy of greece > Hertigdömet Grekland (or better, just Grekland)
Kingdom of Cyprus > Kungadömet Cypern (or better, just Cypern)
Bosnia > Bosnien
Tver > Tver
Trebizond > Trapesund
I would also use "Byzantium", or "Byzantine Empire" for the English.
