Hotspot icon instead of WIFI icon?

When travelling I set my iPhone name and hotspot password to be the same as my home WIFI. This means any other devices that I brought from home (like my iPad) automatically connect to the hotspot as the hotspot network name uses the iPhone name. However, I noticed when I arrived home and disabled my iPhone hotspot (even tried turning my phone off) my iPad still showed the hotspot icon when it was clearly connected to my home WiFi. I see others have had similar issues, but I did not find an answer on how to fix it. Seems like the iPad remembers the network name as once being a hotspot so marks it as such forever.

The clue to the simple fix is that the iPad “remembers” the network name. If I select the i next to my home WiFi network name on my iPad and choose “forget this network”, then reconnect the hotspot icon is replaced with the WiFi icon again.