that's not the purpose of it.
if you don't want it known, don't publish it.
the point of nostr is nobody can stop you publishing it.
Discussion
I want to share my message but would prefer to keep my identity in private. Is that posible if you are just a normal person?
"normal person" who knows how to use tor, yes, you can keep your identity private. though you should be aware that everything you say can create links to your real identity.