MOBILE: Go to your main screen (the one with all your spaces listed) and click the "Settings" icon on the blue task bar at the top of the screen (next to where it says "Your Spaces"). Tap "Edit your Profile" and you can change your First and Last Name in the editable text boxes provided.
WEB: In the "Your Spaces" panel (where it lists all of your spaces) click the "Settings" gear wheel icon in the top left-hand corner. Click "Edit Profile" from the drop-down. If you click directly on your First and/or Last Name listed you should be able to edit the text directly.