The exchange will not notice it unless the person do KYC itself admit it to them. Remember that the change don't have any legal documentation coming from so there's no way for them to determine if you are the original owner or not. Even if they try to detect your IP. There is always a VPN to cover that.
They might. I'm not familiar with the sign up process for Crypto-Bridge, but many exchanges that do not require KYC (not that there are many left), still require a name, email address, country, and sometimes an address. If you have signed up as Robert Paulson with
robert.paulson@gmail.com with a US address, and then complete KYC with documents belonging to Monty Python at a UK address, it's going to raise some red flags. Very likely your account will at least be suspended pending further investigation.
but wouldn't there be potential sort of criminal offenses for this? Faking of documents or something?
Absolutely. This is money laundering 101, to withdraw under someone else's name. There could very well be criminal consequences.
As I recall, Crypto-Bridge doesn't require more than just a username/password setup.
However, if one's username is "shaw1", and one puts down a document claiming to be John smith, that would still raise the same issue as if they did ask for your name.
But I absolutely concur with your underlying point. Fraud to combat fraud isn't a good idea. And as soon as you get caught sending in the wrong docs, then they will have the "moral" high ground to seize your assets. All in the name of combating terrorism.