To further verify that the name in a (for example) Kansas regiment is the Arkansan I think he is, I look to my database to see if he had deserted or been discharged from an Arkansas regiment sometime before he showed up in the Kansas regiment. Goodspeed's biographies are another good source for verification.
I'm a fanatic about verification. When I find a soldier in a "foreign" regiment who appears to be an Arkansan, I enter him in my database with an indication that the information is unverified and only appears on the muster roll. I don't mark him as a "fer sure" until I can get a minimum of two non-regimental sources of verification.
Like I said, it takes a lot of detective work. It's only easy when the regiment I'm looking at was thoughtful enough to list the man's place of residence. Kansas regiments were very good about that -- the wrinkle is that Arkansas refugees who enlisted in another state listed their residence as the place they fled to, not where they fled from. Then it's back to the Sherlock Holmes hat and magnifying glass.