Um, why would anyone sign their own journal or diary? Seriously, why did he sign his name? It's Severus' diary meaning that he is the only one writting it so why would he feel the need to sign it? We already know the entry was written by Snape.
Author's response
Okay, I appreciate the constructive criticism, but that was a bit much. Does it matter? He signed it because he felt the need. It plays into the story later. Move on. Leave comments, but don't nitpick about things that don't quite matter.
~Fallen Avenging Angel