Two different questions get tangled together here: "can I get paid without a company?" (yes, today) and "what about tax and registration?" (separate, and still yours). Most pages answer one and dodge the other. Here's both, straight.
Yes - as an individual/sole trader. A PayFac like paas.build onboards you with a real, capped merchant account the same session (progressive KYB), so you can start taking card and SEPA payments immediately. You remain responsible for declaring income and meeting local tax rules.
For B2C digital sales across EU borders, once you pass the €10,000 cross-border threshold you generally charge VAT at the buyer's country rate, usually filed via the OSS scheme; below it your local rules apply. B2B is typically reverse-charged. paas.build gives you the data and invoicing but does not remit VAT - that stays with you (or with a Merchant of Record if you want it handled).
Yes - operating as a sole trader/individual is recognized across the EU and UK. The payment rails run on UniPaaS, an FCA-authorised Payment Institution; you handle your own tax and any local registration.
Getting paid is the payment rail (a PayFac gives you that instantly). VAT is tax law - separate, and your responsibility with a PayFac. A Merchant of Record bundles both by becoming the seller, at a higher effective cost and the loss of your direct customer relationship.