Notaries are required to follow strict laws when notarizing documents for someone. As a notary it is very difficult when individuals sign with a name different than the name on their current government issued ID. This is especially true for women who have chosen to use their married name but have not changed their government issued identification to reflect that name. If an individual does not have a current government issued ID to support the name they are going to sign with then it is the responsibility of the signer to provide the notary with a creditable witness or witnesses willing to state that he or she knows that person by the other name. The credible witness will sign in the notary book and their information will be noted in the notary book.
The responsibility is on the signer to provide either the ID or witness or witnesses, not the notary. A notary is not allowed by law to notarize any document for any individual who does not have a current government issued ID.