We do recommend this and will help you set it up.  Having an email that reflects your website domain name does a few things.  It reminds people of your domain name, shows someone that you are part of that business and lends a professional touch to your correspondence.  Typically a site has a “catch-all” email (info@yourdomain.com) that catches misspelt email names and email.  You can also use specific email names for specific jobs such as bookings@ for accommodations or forms@ for submissions.  The emails can be set up in whatever email program you use or can be accessed online through the domain host.