I'm a closeted gay in the Navy. If I get married will my chain of command know after I file with personnel?

So I was planning on getting married, but my big concern is that my chain of command will find out I'm gay. I'm not closeted with everyone, but I'm more comfortable at work if nobody knows. Has anybody gotten married in the military, preferably the Navy, and is your chain of command privy to the details (i.e. The name/gender of your spouse)?