Different notaries have different views. I have never seen anyone post, in any of the popular notary forums, a law or official rule from any state that specifies exactly what to do if the name printed in the document does not exactly match the name on the ID.
The law in Vermont, for acknowledgements, says
(a) Acknowledgments. A notary public who takes an acknowledgment of a record shall determine, from personal knowledge or satisfactory evidence of the identity of the individual, that the individual appearing before the officer and making the acknowledgment has the identity claimed and that the signature on the record is the signature of the individual.
(The wording for verifications under oath and signature witnessing are virtually the same)
As I read the Vermont law, if someone comes to me and presents me with a document with the name "Erick D Garcia" printed in it, and acknowledges he signed it, my job is first to verify it's his signature. I can do this by having him sign my journal and comparing the signatures, or sign the document (again, if necessary). The next is to verify that he has a right to use the name "Erick D Garcia". As far as I'm concerned, a person with a driver license that says "Erick Daniel Garcia" has shown me sufficient proof that he has the right to use the name "Erick D Garcia", so I will write ""Erick D Garcia" in the acknowledgement certificate.
I always copy the name from the document to the acknowledgement certificate, exactly. If the name on the ID is different enough from the name in the document that I'm unsure if both names refer to the same person, I will ask the signer to show additional ID that satisfies me, or produce a credible witness. Otherwise I won't perform the notarial act.