Wrong name with @me.com
When I'm sending an email to my self using my iPhone and the suggested email addresses pop up, why is another person's first and last name appear with my @me.com address?
iPhone 6s, iOS 9.2.1
If you are referring to when you are typing your address into the "To" field, this list is generated from either your contacts, or your recent history. If there is an ℹ option next to the listing, you can tap it to delete the entry form your history and fix the issue. If not, locate that person in your contacts and remove your email form their contact card.
If you are referring to the name that appear when you receive the email from yourself, that name is found in Settings > iCloud > Advance Mail (At the bottom) > Name.
Hope that helps.