The email address that you use to identify your Apple Account (formerly known as your AppleID) and your iCloud email address are independent of each other - unless your Apple Account actually uses your iCloud email address to identify it.
By example...
Your Apple Account may use the email address jon.doe@anycompany.com to sign-in to your Apple Account - while the associated iCloud email account that you have chosen might be jon.doe@icloud.com. Changing your Apple Account login to use jon.doe@neworg.com does not change the iCloud email account that is associated with the Apple Account.
Your default iCloud email address can be chosen from the primary email address, or if configured, any one of three aliases which you can create from the page in your illustrated screenshot. While you can add or delete aliases addresses, your primary iCloud email address cannot be changed.
If you wish to configure an entirely different [third-party] email address to use with your email, you simply need to set up the new account in iPad settings:
Settings > Apps > Mail > Accounts > Add Account
The default email account used to send email from the Mail App is set elsewhere in Mail settings:
Settings > Apps > Mail > [Composing] Default Account - select from list
Additional information can be found within the iPad Guide. Here is a direct link to the relevant section of the Guide:
Add and remove email accounts on iPad - Apple Support
Should you need to change primary email address that you use to sign-in to your Apple Account, you can find details of how to do so here:
Change your Apple Account primary email address - Apple Support
You may also find this support page provides useful additional information:
About your Apple Account email addresses - Apple Support