[exim] HELO with short mailname

I send mail from an Exim4 installation, and it's rejected from some MTA
servers with:
"Helo command rejected: Host not found"
because Exim announces with the short hostname instead of the specified
in /etc/mailname (FQDN)

If I run:
dpkg-reconfigure exim4-config
I can change the "System mail name", and it's updated on /etc/mailname ,
but it's not used by Exim on HELO announcements.

How can I make Exim to use mailname instead of hostname?

Thanks.