[Plugin: Email Alerts] Change email address

It’s really a matter of 5 minutes. Just add those 2 filters in your theme functions.php:

Filtering the email address
Add a filter for the email address using ‘add_filter’:

add_filter( 'wp_mail_from', 'my_mail_from' );
function my_mail_from( $email )
{
    return '[email protected]';
}

Filtering the email name
Now add a filter for the name of the email address:

add_filter( 'wp_mail_from_name', 'my_mail_from_name' );
function my_mail_from_name( $name )
{
    return 'My Name';
}

Source: https://butlerblog.com/2011/07/08/changing-the-wp_mail-from-address-in-wordpress-without-a-plugin/