Stopping iMessage from displaying texts and iMessages on my MacBook screen
Have you tried the following from Apple's website:


  OS X Yosemite: Turn off notifications
  
  If you don’t want to see notifications in the top-right corner of your
  screen, you can turn them off. You can turn off notifications for
  certain apps, or turn off all notifications during specified times by
  setting Do Not Disturb. For example, you can turn off notifications
  sent from the Calendar app, or turn off all notifications for when
  you’re asleep.
  
  Turn off notifications for an app
  
  
  Choose Apple menu > System Preferences, then click Notifications.
  Select the app on the left, then choose None below “[App] alert style” on the right.
  
  
  The app’s notifications won’t appear on your screen. If you also don’t
  want to see the app’s notifications listed in Notification Center,
  drag the app down, to the Not in Notification Center list on the left.