How to get latest device names when joining hotspot? iPhone still shows up even though device has been renamed minutes ago.

It is not clear from your post what name you have changed and where.

The Personal Hotspot name on an iPhone is derived from the device name set in Settings > General > About > Name. However, after changing the device name, the new hotspot name may not update immediately. To ensure the change takes effect, try the following:

1. Restart the iPhone – This often forces the system to refresh the hotspot name.
2. Toggle Personal Hotspot Off and On – Go to Settings > Personal Hotspot and turn it off, then back on.
3. Forget and Reconnect on Other Devices – If you're connecting from another device, forget the old hotspot and reconnect.
4. Wait 10-15 Minutes – Some users report that the new name updates after a short delay.
5. Reset Network Settings (if needed) – Go to Settings > General > Transfer or Reset iPhone > Reset > Reset Network Settings, but note that this will remove saved Wi-Fi networks.