Is it a fake contract to sign an agreement with only a surname and no name, because there is an agreement in which a person's first name is only a surname, and there is another one without a signature. If you only sign your surname and don't write your full name on the agreement, it may be that this person has no intention of signing the contract at all.

So ask this person if he wants to make an agreement. If this person really means to make an agreement, then the agreement is only valid if he signs his surname.

As for the contradiction of the agreed date, it is not a problem.