How do i use eponymous in a sentence?

1. The city of Rome is eponymous with its founder, Romulus.

2. The disease eponymous with Dr. Alzheimer is characterized by progressive memory loss.

3. The eponymous hero of the Odyssey is Odysseus.

4. The eponymous flower of England is the rose.

5. The eponymous composer of the Fifth Symphony is Ludwig van Beethoven.