A huge congrats to you, @Satu_TheGreenWitch! 
It is a beautiful name- may you wear it with pride! 
I’ve always been under the impression that your magickal name can be worn openly and honorably- especially when in a safe space like a coven! 
The only magickal instance of keeping names secret that comes to mind is that you should never give your true name to the Fae (more about Working With the Fae here). But names are funny things- one person can have many names! Your birth name, chosen name, magickal name, and true name could, in theory, all be very different things.
In situations like this, I’d say it is up to you to wear the name you feel most comfortable with, @Franklin! 