How can I assign them to users within my Organization?

You can integrate with your bug filing tools such as Jira, Trello, GitHub and Slack and start assigning issues to different members of your organization.

Links

Jira – https://www.browserstack.com/jira-integration

Trello – https://www.browserstack.com/trello-integration

GitHub – https://www.browserstack.com/github-integration

Slack – https://www.browserstack.com/slack-integration