For some reason, Apple decided to screw up Personal Hotspot in iOS 7.1. Right after the update, there's only problems galore across all devices running iOS 7.1. Of course, if you're in the lucky club, your iPhone's personal hotspot feature should work just fine as before.
But if you're facing issues after the iOS 7.1 update, it's mostly because your carrier doesn't allow personal hotspot (or doesn't support internet tethering). Officially, that seems to be the stance. Is there a fix?
Personal Hotspot on iPhone
Personal Hotspot is largely a carrier-based feature. If your carrier doesn't support it, if it actively prohibits you from using it without, say, paying for it, you won't be able to use it. But many carriers either choose to let their subscribers use the hotspot/tethering feature or choose to ignore applying any restrictions actively.
Apple seems to have cracked down on what it sees as personal hotspot “abuse.” Unauthorized personal hotspot tethering doesn't go down well with these folks. If your carrier hasn't arranged with Apple to offer internet tethering, iOS 7.1 most-likely won't let you use personal hotspot. This seems to happen even if the carrier in question does support internet tethering.
On the other hand, if the carrier doesn't have any restrictions as such, personal hotspot might work provided Apple doesn't identify the carrier as unauthorized/unsupported.
At one level, all this does sound insane.
No End In Sight
The thread on Apple's discussion forum now extends to over 20-pages. There's not one solution in sight. Going by the commentary on this issue, it looks like Apple might not even acknowledge this as an “issue”. So, hoping for an update to iOS 7.1 that would fix the personal hotspot problem seems a lot like hoping for the impossible (although we're not dismissing the possibility completely).
If you updated to iOS 7.1, there's no way of going back. Your iPhone can't downgrade to iOS 7.0.6. That option, therefore, is ruled out.
However, you could call your carrier to verify if personal hotspot is enabled/active for you. And possibly, they can fix it for you in case it's just a matter of authorization from carrier's end.