The issue you're talking about is: User agreed to pass the KYC-check, but the personal information, provided by him earlier was innacurate, so he can't complete it. This is only one aspect of this story.
But this is not the case, i'm talking about.
From one side, the exchange can ask for a mandatory KYC-check (normally with a notification in advance, which was not done by Traidsatoshi).
From the other side, user can deny to pass it. In that case he won't be able to trade anymore - this is ok. But, all the funds he had before KYC were deposited or traded by him under the Level 1 verification from Tradesatoshi, so they are all legal. So all this funds must be returned to the owner. By now Tradesatoshi is denying users to withdraw their funds, which is totally unacceptable!
Ultimately if you have used their platform - you agreed to the terms. By registering with a false or incorrect name or details you committed a fraudulent act or made a serious error when entering a contract.
Usually people don't need to "change their name details" unless they gave false details.
It is something you will need to sort out through their support ticket system. Ultimately though it comes down to a user error. (Deliberate or not)
The only way to check whether someone gave false details is to ask them to verify their identity which appears what they have done and appears consistent with their terms.
People will have opposing views on this but registering (entering into a contract) with a false name (alias) is a crime in some jurisdictions.