Welcome to the forums,
Ok so it is kinda an advertisement for us by default - but we do allow the modification of:
/opt/zimbra/mailboxd/webapps/zimbra/WEB-INF/classes/messages/ZmMsg.properties (or respective for language) ZmPrintView-company is composed of: buffer[_i++] = ZmMsg.zimbraTitle ; (by default 'Zimbra') buffer[_i++] = " "; buffer[_i++] = ZmMsg.splashScreenAppName ; (by default 'Collaboration Suite') Thus you see "Zimbra Collaboration Suite" when printing. See this RFE which is requesting the ability to toggle on/off 'print full header' TRUE/FALSE pref - where it removes everything including the from/to.
-Though one of the dupes is asking for options to adjust how much of the Header (To/CC/From) is printed I doubt we'll do that much into a pref anytime soon. Removing just the company header & username doesn't save much space, plus it tells you who printed it in-case it's not apparent by a crowded to/cc, and for the people who really want to circumvent that they can just copy into a word editor.
Bug 9379 - Web GUI Printing: Remove Zimbra Header
EDIT:
To take some of the work out of updating the desktop client for everyone in the future, vote for
Bug 22291 - Allow rebranding of Zimbra Desktop Client