How do I change my name so that my outgoing email says the name I'd like it to to the receiver?
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You can change that in mail’s preferences.

To do so:

go to Mail (in the menu bar at the top.
Select “Accounts” then select the email address who’s name you’d like to edit.
Select “Account information”
Select “Email address” then choose “edit email address”.
Click on the name on the left then change it.