To update your setting preferences to make your birthday or work anniversary private, click on your name on the left side bar to enter your profile settings

Then, go to the Personal Information tab, which lists your user profile information.*

Scroll down until you find the Birthday and Hire Date section.

If you want to make either or both private, you will check the box that says Keep my birthday/work anniversary shoutout private.

Then make sure to press the Save Changes button.