[exim] Outgoing From header field format

What configuration within exim defines how the outbound From header is
formatted?

What I mean is whether the header has just an email:
user@???

vs. a name and email in brackets:
A User <user@???>


I'm asking because I have several machines that send nightly status
messages where only a couple of the machines send with the second format
(specifically it sends out: root <root@host>) while the others simply
send out root@host.

All but one machine is configured to use a smarthost. Of those
satellite machines, all but one sends out using the name/email format
and uses only my domain (full format is "root <root@domain>). The one
satellite machine simply sends out "root@domain" without a name. The
smarthost itself also sends out its own messages but it uses
root@??? with no name.

The same programs run on all the machines (file system checks,
antivirus, etc.) so they would all be using the same outgoing message
format. I've tried to compare the exim configurations of the satellite
hosts and they all seem to be using the same settings. The /etc/passwd
files all look the same for the root account.

It's not affecting mail delivery but it's just odd that the machines are
somehow slightly different and I'd like to understand it better (and
partially because it bothers me to see a list of emails that have
slightly different From headers but that's just an OCD thing).