Great, you have now committed fraud. You just went from tax dodger to hardened criminal.
You'll have to show a copy of your passport or other ID document with this new, fictive ID number. So let's add forgery to the list.
Depending on country but pretty much all have ways to verify that ID numbers are valid, either through check numbers (the number is generated through a verifiable algorithm) or through online registers to which financial institutions have access.
But suppose you do it and manage to tell your Belize bank that your ID number is 1235 instead of 123S, and that somehow it doesn't get manually or automatically detected as invalid. The information is still going to be shared and end up in the hands of the government in whose country you live (and/or your country of citizenship). At that point, you're at the mercy of that government's systems not identifying you by name, address, ID, date of birth, and other information in case they have a fuzzy matching system or manual review process.
And all this for what? To illegal save on taxes but at the same time opening yourself to having your funds frozen and potential prison time and fines?
Those who adapt to the present will do much better now and in the future. Get stuck in the old ways of secrecy and tax evasion, and see what happens.