ICloud :: Mobile To ICloud Wrong Name?

I had/have a family pack Mobile me account.we shared itunes music apps etc and of course had separate emails I followed the instructions to transition to the icloud so we could continue  to share apps and music but have separate email accounts, calendars etc we have ipad/iphone/desktop.

when the secondary person sent emails my name  was appearing on her email with her email address.  I went deeper into "settings on the ipad and iphone and changed the name for emails.  I think that solved it. 

when I go under the apple on her desktop to system preferences to: icloud  it has the wrong name.  I can go into account details and type her name in  but the grayed out name under the icloud is still me and when I go back to account details it reverts back to my name 

when I go to mail contacts and calenders her name and account is correct for the mail but again, the icloud is incorrect...has my name. She does not have my calendars or contacts and I don't have hers