I want to change my password Apple ID (for another account on my mail), but do not send a letter about the password change Apple ID, what to do?

Try this:

To change your Apple ID, follow these steps:

1. Go to My Apple ID (appleid.apple.com), click "Manage your Apple ID", and sign in.
2. If you have two-step verification turned on, you'll be asked to send a verification code to the trusted device associated with your Apple ID. If you are unable to receive messages at your trusted device, follow the guidelines for what to do if you can't sign in with two-step verification.
3. In the "Apple ID and Primary Email Address section," click Edit.
4. Enter the email address you want to use, then click Save Changes. Apple will send a verification email to that address.
5. Open the email from Apple, then click Verify Now in the email.
6. When the My Apple ID page opens, sign in with your renamed Apple ID.
7. If you have two-step verification turned on, you'll be asked to send a verification code to the trusted device associated with your Apple ID.