Multiple Wordpress domains - wp_mail - hostname

How can I setup postfix to have the FROM address in the form of a WP domain/user, instead of the /etc/hostname?

Currently gmail marks the message in original source as

mailed-by: myhostid.hostingprovider.tld (/etc/hostname)

signed-by: mydomain.tld

…and it mostly goes to spam, even for the password reset messages.

I have SPF, and DKIM set up.