To connect to a hotspot you need not use the same Apple ID / iCloud ID.
Use these steps first
Restart the iPhone or iPad that provides Personal Hotspot and the other device that needs to connect to Personal Hotspot. Make sure that you have the latest version of iOS. On the iPhone or iPad that provides Personal Hotspot, go to Settings > General > Reset, then tap Reset Network Settings.
If Personal Hotspot is not working on your iPhone or iPad (Wi-Fi
Hotspot is carrier specific feature. Contact you carrier.