At the moment, one’s empire is only really distinguishable from other empires by the shield.
How about this: if one’s empire reaches a threshold of contiguous hexes, you can enter some information about it. So tapping on ‘Inspect’ reveals the name of the empire and even some history.
So you have to earn the right to name the empire: some extra incentive.
We could also distinguish empire sizes by colour, maybe. At the moment, it’s difficult to distinguish between different empires looking at the map: all conquerable territory is the same colour.