The other option is to put it in a circle and just leave it with white background for the favicon, like these other logos are circulr and it looks decent. or, if you want the purple to stand out more, like the other favicons here, that's an entirely different design. 

https://image.nostr.build/ca09e1b441ea2b76bd8497a9a4dfc974277b7e98ff4395af85db24ed5b548488.png