According to European AML directives, KYC regulations, and platform requirements.
It would be better if you include information on the site that this service complies with European regulations. Don't know which rule you're referring to, just found this European AML policy update:
They set limits up to €7000 for cash payments and €1000 for crypto-asset transfers, where the customer cannot be identified.
https://www.europarl.europa.eu/news/en/press-room/20230327IPR78511/new-eu-measures-against-money-laundering-and-terrorist-financingYour opportunity to serve customers with privacy is €1k. More than that you're putting the customer at risk of requesting verification.
Overall, you really can't promise privacy guarantees as long as you comply with any regulation. You know, they hate privacy.