It is good Netiquette to include your full name. Do put your first and last name.
Name Netiquette Signatures
A signature at the end of a message gives it authenticity. The concept of an email signature is similar to a letter, in theory. An email signature is different than a written one in practice. Email signatures are typed. They begin with the name of the author. There may be a lot of other information.
A name makes the message official, it signifies the end of a document. It’s the authors approval of the above text. This alone gives it authenticity if you know the author well. The remaining information in a signature makes it credible.
Name first because it gives the message approval from the author.