By request, I’ve found a way to allow commenting on posts. This isn’t something that is built in to Tumblr. The service is called Disqus, and you should be able to login with your facebook, twitter, or google account. If not, I’d encourage you to use your real name to help us keep discourse on the site civil.
If it’s not immediately evident, all you have to do to comment is click the text that says something like “0 comments and 0 reactions” under any post to enlarge the comment field.