If a document doesn't have a notarial acknowledgement the notary may simply affix their stamp and sign their name?

No, a notary cannot simply affix their stamp and sign their name without a proper notarial acknowledgment. A notarial acknowledgment requires the signer to personally appear before the notary and affirm that they signed the document voluntarily. The notary's role is to verify the identity of the signer and ensure they understand the document, which is not fulfilled without the acknowledgment process. Therefore, without this acknowledgment, the notarization is not valid.