Once I turn on a hotspot in Settings > Personal Hotspot, on iOS, and a device connects, a blue banner at the top of the screen appears with the number of connected devices. I would like to see the hostname and any other associated information about the devices connected. Where could I find this information?
While you can't see a current list of what is connected to your iphone's personal hotspot, you can goto Settings/Cellular/go down to the CELLULAR DATA section and click Personal Hotspot that has a Data amount next to it, and you will see a list of each device and the amount of data they have used on the hotspot.
Unfortunately no GUI exists in iOS for finding details about connected devices to the wireless hotspot (i.e. tethered devices). You can use a network scanner app to find connected devices, but it is not fool proof as it will only find devices that actively respond. Usually you'll only be able to find the MAC address and the IP-address given to the unit.