Your profile is shown to only the verified users hiring at their own companies. Third party recruitment agencies are not allowed to view your profile.
By default, your profile is hidden from your current company. You can always add more companies in that list.
If you do not want anyone to see your identity, you can go "under cover". Employers will only see your profile headline, skills, location, company and profile summary. Your identity will be shared with them only when you respond to their messages.