How to make Xbox gamertag private

I’m trying to make my Xbox gamertag Not searchable.
My Activision ID is private but I want my gamertag also private
I’ve gone on the cod app and changed both settings to “just me” and I’ve also gone on the website and changed all settings to everyone and then back to “none” but I can still search my gamertag… how do I make it private

So to clarify my Activision ID is PRIVATE which is perfect
BUT my Xbox gamertag (so wishful) Isn’t private
So how do I make it private thanks