Can I change the visibility of my leaderboard?

Yes, you can decide whether you want a public leaderboard or a rather private one. 

To change the visibility of your kudos leaderboard, go to Kudos > Kudos Settings. Find the option Leaderboard visibility and select the option that fits you the most.

You can select between having a public leaderboard, one visible within teams, or just by org admins and managers: