Each time a song starts a notification is sent on the desktop. So I have two notifications in the gnome panel: the normal song playing notification with play/pause, and a normal notification with the name of the song. It shouldn't have the second notification with the name of the song. It's pretty minor but a bit annoying, like when my computer is asleep it wakes up to display the spotify notification. No other app does this. I'm using the spotify app instead of the website mainly to listen on an external speaker.
Option 1 - In Spotify top right under username go to:
Settings > Display >
Disable "Show Desktop Notifications when a Song Changes
This will prevent Spotify sending that second notification, the current song notification with player controls will still be there, but will not pop up as a notification each time. this should also stop notifications on the lock screen, but if this still occurs, go to the Gnome Settings App
Notifications > Spotify >
Disable "Lock Screen Notifications" and any other settings that you don't want