Apps do indeed have to have unique names. If a desired name isn't available, developers commonly solve the problem by adding a bit of description to the name, making it unique, e.g. "SuperText - Text Editor for Geeks" when "SuperText" isn't available.
Until recently there was a significant name-squatting problem, with devs creating placeholder apps that tied up names indefinitely. Apple cleared all of those out last Fall, making a large number of names available again. Now an app created in iTunes Connect but not submitted for review will receive a warning after 150 days and if there's still no submission 30 days later, the placeholder is deleted and the name is freed up to other developers (as per the policy you quote). Significantly, that specific name is no longer available to the developer that first used it, so be certain you're going to submit soon after creating the app in ITC.
As to approved and then later renamed apps, I don't know what Apple's policy is, and it's not spelled out anywhere that I've ever seen. I think it's somewhat unlikely that the old name becomes available due to potential consumer confusion, though: "I bought 'Buddy's Checkers' but now it's saying that I didn't buy it."
Note: Updated from 90 days to 150 days, per Apple's change. See "App Name Expiry" in the iTunes Connect Developer Guide. (thanks to Alexander)
