You can use your Apple ID on multiple devices at the same time.
If you have a lost a phone you may wish to remove your data on it to maintain privacy and security. However, you may wish to leave Find My set up on it and possibly even leave a message for finder to contact you (make sure you don't open yourself to scams if you do this).
Click on this link for general information about what to do "If your iPhone, iPad, or iPod touch is lost or stolen" --> https://support.apple.com/HT201472
- The Find My service is the only recovery feature Apple offers. It MUST be set up before the device is lost. If you did not do that it is too late to do it now and there is no other feature Apple offers that can help you find it.
Use Lost Mode in Find My iPhone on iCloud.com - https://support.apple.com/guide/icloud/use-lost-mode-mmfc0f0165/icloud
and:
Use the Find My app to locate a missing device or item - https://support.apple.com/HT210515
"What happens if you activate Mark As Lost
Mark as Lost remotely locks your missing iPhone, iPad, iPod touch, or Mac with a passcode, keeping your information secure even if your device goes missing. You can also display a custom message with your phone number on the Lock screen, and keep track of your device's location.
Once Mark as Lost is activated, Apple Pay is disabled, if you have it set up on the device. A confirmation email is sent to the primary email address associated with your Apple ID. When you recover your device, you will need to unlock it with your passcode."