Can I remove recently played songs on spotify

Spotify is one of those company who provides a lot of features late their system.Like currently their is not a proper way to change spotify username. Just like that currently their is no method to remove a recently listened songs from your spotify play history. You can follow the steps mentioned in this post which explain how you can access spotify play history on different devices.
After accessing spotify listening history. Right click on any song you'll not find any option to remove or delete song from play history. But you can remove songs from your liked songs from spotify listening history.

 Can I remove recently listened songs on spotify mobile app?

Just like desktop app currently, there are no option to remove songs from recently played section in mobile app also. If you are not able to access play history on mobile then kindly visit the link above.

Can I remove recently played song on spotify web player?

Spotify web player doesn't have option to access the listening history. That's why you can't access and delete or remove a song from listening history on spotify web player.