I would change the name of my mail

For iCloud: Settings > Password & Accounts > Tap [Your Name] > Contact Information > Name [Change]

For Gmail: Settings > Password & Accounts > Account > Name [Change]

If you want to Change the Description of the Mail, Description [Change]

For Exchange:: Settings > Password & Accounts > Account > Name [No Option]

If you want to Change the Description of the Mail, Description [Change]

For Outlook:: Settings > Password & Accounts > Account > Name [No Option]

If you want to Change the Description of the Mail, Description [Change]

For Yahoo: Settings > Password & Accounts > Account > Name [Change]

If you want to Change the Description of the Mail, Description [Change]

For AOL: Settings > Password & Accounts > Account > Name [Change]

If you want to Change the Description of the Mail, Description [Change]

What do you mean by change the name of your mail? Do you mean your email address? See if this helps: https://support.apple.com/en-gb/HT202667