If you click Start on a story, you will automatically become its owner. A story can have up to three owners at any given time. For instance, a story might be owned by a developer pair plus a tester, or a by developer pair and a designer.
To add an owner, just click + to the right of the Owners row in an expanded story.
To remove someone, click their initials in the Owners row, then click Remove.
You can see stories that you own but aren’t actively working on in the My Work panel.