First you must realise that Chicago, Miami, and Spokane are cities, not states – that is why the sentence is in two parts.
In this sentence “as were” means “and so were”. It is saying that those states were named after tribes, and the cities were named after tribes too.
Paraphrase? I don’t think you can make that sentence much shorter without leaving out the names of the states and/or cities:
Also, I used the more modern term "Native Americans" rather than "Indians".
- Some states and cities were named after Native American tribes.