It’s good branding. “China,” as we think of it, fragmented into states that recombinated into different versions of what they each claimed to be the rightful empire, many, many times. It’s like a ship of thesius thought experiment, almost, but sometimes the boat is a pile of wood, sometimes it’s a galleon, other times it’s a fleet of smaller boats.

And sometimes it’s Turkish. (Sorta)

Source: degree in Song Dynasty era Chinese history. (It’s a long story)