Open Profile from the More menu or Settings. You can add an optional display name, profile photo and birthday.
Your shared profile is only visible to people connected to you through an accepted shared calendar. Your email address and private organiser data are not shown on the profile.
Birthday privacy can stay Only me, or you can choose People I share calendars with. A contact in your Address Book whose email matches an Organise You account is linked to that account, and a View profile link appears when you also have an accepted calendar-sharing connection.