To rename your iPhone's Personal Hotspot, you need to change the name of your iPhone itself. Here's how:
- Open the Settings app on your iPhone.
- Tap General.
- Tap About.
- Tap Name.
- Delete the old name and type in the new name you want to use for your iPhone and, therefore, your hotspot.
- Tap Done on the keyboard.
Your Personal Hotspot will now broadcast the new name. Keep in mind this changes the name of your iPhone, not just the hotspot. So Bluetooth connections and other services will also reflect this new name.