My first and last names are in my e-mail account names. Even so, when I e-mail someone I don’t know personally or know only formally and in a business context (say, a prospective client sending me an inquiry), I always use first and last names. That’s a matter of courtesy.
To friends and family I use only my first name.
If my e-mail account name were essentially anonymous, I would always include both first and last names when writing to anyone I wasn’t certain would know my account name, even if we’d corresponded before.
I don’t like getting a chummy message from someone with an account name like “linda54321’ or ‘mrcool’ who just signs off “Linda” or “Joe” and expects me to know them if they haven’t given me a clue. As far as I’m concerned, that is spam.
In this context, you can’t go wrong giving too much information, but you can certainly go wrong giving too little.