Hi Edward! That's not part of Tableau Server's native functionality. However, perhaps it could be accomplished out by using a separate generic web server (installed on a different host than Tableau Server) which supports redirects. You'd configure a web server so that if someone comes to marketing.company.com, the web server hosting marketing.company.com simply redirects the browser to the desired URL on Tableau Server, such as reports.company.com/sites/marketing, and so on.
We have a redirect like this on our website: if you go to http://support.tableau.com, you'll end up being sent to http://www.tableau.com/support. That's just using our web server software; Tableau Server isn't involved at all.
The details of how to do this would depend on the web server, so it'd be best to check with a friendly web server administrator in your company. Here's a tutorial I found for doing redirects on Apache - but your friendly web server admin no doubt knows much more about setting up redirects than I do!