To edit your Share ID, open the 'Account' window in your SpiderOak client, or, after logging into your account remotely via the Login link at SpiderOak.com - choose the 'Account' tab on the SpiderOak website. Next to your current ShareID you will see an "Edit" button. Click this to reset your ShareID.
It is not possible for you to edit the "Name of Person Sharing" which appears at the top of this share. This will always by default display the first and last name you gave when signing up for the account. If you absolutely need to change this information, you would need to open a new account.