To notarize someone, they have to be either personally known by you or have their identity proven on the basis of satisfactory evidence. Satisfactory evidence usually means that the signer produces a valid and current identification document or card with a photo, signature, expiration date, and physical description issued by a government agency.
Credible witnesses
However, some states allow for a signer to be identified by credible witnesses who swear to the identity of the signer. Unfortunately the witnesses might not know the person's exact name and will swear to any name variation. "Sure, he's Fred M Smith, isn't that who he is? Fred P Smith, okay... I swear that he is Fred P Smith".