Simply not Telling Your Name
If you do not want somebody to know you -- or at least not your name -- you can, quite simply, not tell it. If you do have to give a name, you can make up one.
With email you have to give a name in the From: field of any message you send. It is you, however, who controls what this field tells. You can state a wrong name, and you can state a wrong email address.
If you change only the name, there are only very few that you can fool. Your email address will lead to you (and, alas, your name).
If you give a wrong email address, too, the level of anonymity is increased. At first look, nobody will know a message is from you (unless, of course, you forget to remove your signature or have such a characteristic writing style...).
The price for increased anonymity is that your email address is wrong and thus you won't be able to get replies to your messages.