On the MLS, yes it will be available for agents so they can contact you directly for showings. In some cases your broker may also be able to include your email address. On “public” websites, such as Zillow, Trulia, or Realtor.com, only the listing broker contact information is allowed to be displayed. The MLS has rules about what information is allowed on 3rd party websites. Neither you, nor your broker can do anything about this, and these rules are strictly enforced.