Some people have a religious name that they are known by within the entire pagan community. Some people have a religious name that they only share with those of their coven and use during ritual. Some have two religious names. It's really up to you. Some people feel that they can be more easily cursed if others know their craft name. Some people feel that keeping their craft name a secret between their coven and Gods make it more sacred. It's really about what feels right to you.
If your coven wants you to have a religious name that is known to only the coven, you could always have a second, more public, religious name.