First, we close messages with a mark. Then, its our brand for what we are called in the first place. After, our surname is included for a stronger identity. It follows, the seal at the bottom. So, full name for reference in digital signatures. Given, good netiquette to include our seal mark. As a result, do put your first and last name.
Next, a signature at the end of a message gives it authenticity. Then, the concept of an email signature is similar to a letter, in theory. However, an email signature is different than a written one in practice.
Hence, email signatures are typed. Thus, they begin with the name of the author. Therefore, may be a lot of other information.
In any event, a name makes the message official. And so, it signifies the end of a document. Also, that the author approves of the above text.
Then, gives it authenticity. Provided, we know the author well. On the other hand, we can do a search. Thus, remaining information in a signature makes it credible. More stuff that can be validated.
Full Name Netiquette
Name first because it gives the message approval from the author.