Try leaving the From Display Name blank in the Email Password server behavior.
Keep in mind that if you edit the server behavior, the mail_PHP.php file will be overwritten, you will need to add the -f argument to the mail() function call again.
make sure the email is not being trapped as spam also.
If all else fails, check with the host. Ask them to look into the SMTP server error logs to see why the server is not relaying the email.