Don't forget when you register a new account in a centralized site, they will record your real IP address, your device, which internet provider etc that you won't know. They mostly not allow you to mask your IP address e.g. using VPN, VPN isn't a good way for privacy.
As long as you're can't use Tor, I don't think it's private.
Here in Philippines,
Sim card registration under the owner ID is now required which means a simple phone number that given away on any services is considered a full KYC because we submit full KYC on our phone number here. All sim card that is not registered will be expired and not usable after the given deadline date.
It's not only happen in Philippines,
but there are around 160 governments are enforcing mandatory SIM card registration. I don't think they will really force it and SIM card that is not registered will not usable anymore, there's should be a way either the SIM card is already registered from the beginning or there's a not really strict provider.
The "Basic information" that most exchanges ask for entry level KYC verification (such as phone number, email address, Name, Country)can actually be forged and even edited if the exchange has not yet implemented mandatory KYC verification. So, I personally find such Information not a big deal.
If you check on their terms, you will find if you need to use your real name when you creating new account. So if you're using a fake name or alias, you will have a problem when the exchange ask your ID card. If you're using your real name, the exchange has a chance to find you especially if your name are unique.