Q: How do Change the name of a mailbox iOS8?

Hi Befromlondon,

To change the name of the account - iOS calls that the description - go to Settings > Mail, Contacts, Calendars > select the account > select the Account at the top > select Desctiption > delete the old name and enter the new one.

It is similar to the process of setting up a new account, described in this article -

Add an email account on your iOS device

Thanks for using Apple Support Communities.

Best,

Brett L 

Hi Befromlondon,

Thank you for using Apple Support Communities. Due to the nature of the issue you described you may find more information by using another one of Apple's support resources - https://getsupport.apple.com/GetproductgroupList.action.

Brett L