Currently, it is not possible to change your profile name or picture directly on the community site. If you've signed in with a social provider (e.g. Google/Facebook), then updates you make to that account will propagate here.
However, we do have a pending feature request ticket in for this, but unfortunately I don't have an ETA on when this will be available. I'll make an update to the ticket to include modifying profile name as well.
Thank you for the feedback!