I think this question would be much better suited for /r/history or something less formal than this sub.

But off the top of my head there's the Babylonian Empire. Alongside this, a large amount of former states are only called what they are now due to modern historical convention, so really the Delian League can be called the Athenian Empire and you're not too far off from what it really was.

Technically the question your asking is trivia, but it's also misguided by the way you are framing it.

Rome was not a 'state' of which 'Rome' was the capital. Rome began as a city-state and so the Roman Empire was Rome. Don't think of Rome as the capital of a larger national entity.

It's hard to come up with a modern parallel. But I suppose you could speculate one into existence. Say the city of London went rogue, declared its independence from the UK, and set itself up as a modern nation-state. And then it decided to start conquering territory. Such as, the rest of the British isles. All that conquered territory now belongs to the entity of 'London', and I guess we would call it 'the London empire' or something.

What first comes to my mind are smaller duchies, although they aren't exactly 'empires'.

Most, although far larger than a single city, held the namesake of their capitals for their entire history. Some were of relatively large wealth and historical importance, such as Venice (Venexia) or Saxony (Sachsen).

There are a couple others, though.

The Byzantine Empire was named after Byzantium, which was the original name of its capital city before the reign of Roman emperor Constantine.

The Kievan Rus was named after Kiev, its capital and most important city.