As far as I can tell, no, this screen does not have any customization options. That said, if you can get past the word "Version", this may still work as you would like.
For example I use a kanban board to manage personal requests from my team. While I don't have have versions in the sense of a software project, every Friday I make a new release named like "2014, Week 39" that contains all the things I've done. I then create a quick blog post on my personal page in Confluence using the JIRA report macro, add a few comments, and publish for everyone in our company to see.
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