We use Confluence, a great tool for user stories! It works like a Wiki, but with richer UI and functionality.
Confluence can be used as an intranet and at the same time be accessed outside of the company via Internet.
Enable quick collecting of story titles
Confluence have built in macros like table of content and other useful content containers such as children display.
Enable to map/share/group the collected stories
You can filter content by users, groups, labels and tags, which is shared instantly.
Allow open discussion around stories
Every page have comments, which is threaded if there are many comments.
Enable collaboration for collecting stories and elaborating their meanings
Since it’s a Wiki, you can