How do I check which forum is installed on my site?

In most cases it's part of the Disqus code on your site. Example: dsq.src = 'http://my-shortname.disqus.com/embed.js';

Your shortname is in your Appearance settings under 'Disqus shortname', if the theme came with the Disqus code installed.

Under the Disqus plugin's Advanced Options, the Disqus shortname is listed near the top.

Go to Design > Edit HTML. Check 'Expand Widget Templates' (right above the HTML code box) and find this line: var disqus_shortname = 'my-shortname';