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.
I remember when I signed up for Poloniex in 2014 I gave them a fake name, because I didn't necessarily trust them, as most people didn't. Then when their Circle acquisition came and they insisted everyone do KYC, I said screw that, because where I lived didn't even allow bitcoin exchanges and Poloniex would have certainly taken that into consideration. Poloniex also gave me the option of changing my customer name, which Trade Satoshi does not. They let me withdraw my coins, and I moved on. This is the standard I'm used to... It seems to me when an exchange uses KYC as an excuse to with-hold customer coins, something fishy is going on. BiteBTC has been engaging in the same behavior.
Then as was pointed out, some people performed the KYC to the best of their ability and were still denied access to their funds. I strongly believe Trade Satoshi recently turned to the darkside as they've racked up a huge number of complaints on social media as of late. They've always had their share of unhappy customers, but now they have way more than their share.