That's another good example of language engineering.

If a crook fools a bank into giving them money, the bank is the victim of the theft. It should be one of the banks primary responsibilities to authenticate the parties to whom they give out money. But if the crook is good enough, it's fair to say the bank is the victim.

But instead they say "you are a victim of identity theft" in order to make you the victim.

The difference being that using someone using your identity fraudulently legitimately has a real, tangible impact.

..You could also make the case that it deprives you of the ability to use your own reputation.

If I copy something of yours, the impact to you is zero.

It's not like you lose your identity as a person though. And i think that that intellectual "property" belongs to the issuing authorities (government, banks etc) not you per se

The correct word for "identity theft" is "fraud", which is what it was called for centuries. Person A pretending to be person B isn't new, and has always been nothing more than a class of fraud, but at some point somebody decided an ancient crime needed a trendy new name.