" I'm asking if things done with this ID number can be somehow hidden from the original owner of the ID number "
If the ID number is yours then take the viewpoint that the ID number is being used to do things or trying to do things that you cannot see.
Overall the question is a question that you need to ask to whoever issues the ID (Identity) numbers.
What safeguards and notifications does the issuer provide when "things are done"?
For example, my bank will notify me if any transaction exceeds a certain amount of money.
Other accounts notify me if there is an attempt to access my account or if account access has occurred.
Or use of the Identity number triggers either a confimation text, email, or phone message. 2 Factor Authorization.
And depending on the nature of the ID number the local authorities (per @rgd1101
may indeed be able to provide some information or guidance.
Especially if the ID is perhaps a driver's license or some sort of local licensing number.
Contact the ID number issuer.
Closing thread to further posts.