I have this issue with dreamhost as well. The WP Mail SMTP plugin worked to fix this for me. Although it's worth noting that on the first day my WP site was up with dreamhost, I experienced an email delay of 3-6 hours. Emails were completely erratic the first day my site was up and running. So I would recommend waiting 24 hours after site install to even BOTHER trying to fix these issues if you are dealing with a fresh install. Because the email delay will keep you from knowing if it worked! See note from dreamhost customer support.
This is related to our SPAM prevention policy. It states that the FROM
address in any form must be an email on the same domain. For example, something like firstname.lastname@example.org.
You can view all bounced emails in your FTP account. Once logged in under your username, click in the the folder /Maildir/new. Here you'll be able to open your messages and see the errors reported as to why they were not delivered.