Others may disagree, but I always put the name in the certificate exactly as it appears in the document. If the name on the ID is different, I must be convinced that both versions of the name refer to the same person. If I'm not convinced, I won't perform the notarial act. My job is to decide if the person before me is the same as the person named in the document.
My state has passed the Revised Uniform Law on Notarial Acts. The Uniform Law Commission's version has commentary, including some commentary about name variations:
Identification of an individual based on an identification credential requires some flexibility. For example, it is not uncommon that an individual’s name as used in a record may be a full name, including a full middle name; however, the name of the individual as provided on the identification credential may only use a middle initial or none at all. The inconsistency may be vice versa instead. The notarial officer should recognize these common inconsistencies when performing the identification of an individual. However, if a notarial officer is ultimately uncertain about the identity of the individual, the notarial officer should refuse to perform the notarial act (see Section 8.)