You have two names on School of Everything: your account username (e.g. 'jennym'), and your actual first name and last name (e.g. 'Jenny Morecombe').
You can't change your account username, but the name that appears at the top of your teaching and learning profiles is editable from your learning profile:
1) Sign in and go to your learning profile.
2) Click edit and at the top of the page you will see a box for first name and last name. The names you enter here is the one that appears on your profiles.
3) Enter the appropriate names, click the submit button at the bottom of the page and your learning profile name will be updated.
There's a bit of quirk here, though - in order to make the new name show up on your teaching profile, you'll need to visit your teaching profile, then click on 'edit' and 'submit'. Your name will then automatically be updated on your teaching profile to match your learning profile.
Your username also appears on your learning profile until the first time you edit it - then it will switch to first name/last name. (There's no good reason for this, it's just a glitch that we hope to fix one of these days.)