I need help with this too, but the only option I can find under "Personal Information" is to change my business name. I have a typo and would like to correct It without having to start over with my online shop, etc.
@CKinkade Sorry for the late reply here,
Unfortunately you aren’t able to edit the legal name you used to activate your Square account. If you'd like to fix a typo with your activation name, you'll need to create a new Square account.
Fortunately the activation name is not public facing in any way.