FWIW, I changed:
My Hostname, My Origin, My Domain to all be "coocooforcocopuffs.com"
Results of postconf -n
alias_database = hash:/etc/aliases
alias_maps = hash:/etc/aliases
command_directory = /usr/sbin
config_directory = /etc/postfix
daemon_directory = /usr/libexec/postfix
data_directory = /var/lib/postfix
debug_peer_level = 2
debugger_command = PATH=/bin:/usr/bin:/usr/local/bin:/usr/X11R6/bin ddd $daemon directory/$process_name $process_id & sleep 5
html_directory = no
inet_interfaces = localhost
inet_protocols = ipv4
mail_owner = postfix
mailq_path = /usr/bin/mailq.postfix
manpage_directory = /usr/share/man
mydestination = $myhostname, localhost.$mydomain, localhost
mydomain = coocooforcocopuffs.com
myhostname = coocooforcocopuffs.com
myorigin = coocooforcocopuffs.com
newaliases_path = /usr/bin/newaliases.postfix
queue_directory = /var/spool/postfix
readme_directory = /usr/share/doc/postfix-2.10.1/README_FILES
relayhost = smtp.office365.com:587
sample_directory = /usr/share/doc/postfix-2.10.1/samples
sendmail_path = /usr/sbin/sendmail.postfix
setgid_group = postdrop
smtp_generic_maps = hash:/etc/postfix/generic
smtp_sasl_auth_enable = yes
smtp_sasl_password_maps = hash:/etc/postfix/sasl_passwd
smtp_sasl_security_options =
smtp_tls_CAfile = /etc/pki/tls/certs/ca-bundle.crt
smtp_use_tls = yes
unknown_local_recipient_reject_code = 550
Email Header (partial) from email that was sent out with these changes:
Received: from DM5PR08MB3610.namprd08.prod.outlook.com (10.164.155.16) by
DM5PR08MB3610.namprd08.prod.outlook.com (10.164.155.16) with Microsoft SMTP
Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA384_P256) id
15.20.77.7 via Mailbox Transport; Sun, 24 Sep 2017 22:31:07 +0000
Received: from DM5PR08MB2604.namprd08.prod.outlook.com (10.173.221.16) by
DM5PR08MB3610.namprd08.prod.outlook.com (10.164.155.16) with Microsoft SMTP
Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA384_P256) id
15.20.77.7; Sun, 24 Sep 2017 22:31:06 +0000
Authentication-Results: MyRealDomain.com; dkim=none (message not signed)
header.d=none;MyRealDomain.com; dmarc=none action=none
header.from=MyRealDomain.com;
Received: from coocooforcocopuffs.com (My.Real.IP.Address) by
DM5PR08MB2604.namprd08.prod.outlook.com (10.173.221.16) with Microsoft SMTP
Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA384_P256) id
15.20.77.7; Sun, 24 Sep 2017 22:31:05 +0000
Received: by coocooforcocopuffs.com (Postfix, from userid 995)
id 945C818538142; Sun, 24 Sep 2017 18:31:02 -0400 (EDT)
So, I would say that My Hostname, My Origin, My Domain, depending on the servers your transit through, may not be so critical, and may not prevent your emails from going through. Just an interesting test to help narrow down possibilities.