Bruce Wayne did not want to be known as Batman, Clark Kent did not want to be known as Superman.
They have aliases.
So should you!
It’s cool to be called Batman online. If it’s really important, your friends know you’re Batman and Bruce Wayne, they can give you a call on the bat phone.
Other people you meet face to face can address you by your given name.
Don’t make it easy for The Enemy to find you online. Be discreet.