Our Destiny Passwords

Am I being too nervous? -- are our Destiny passwords too easy to crack? I can imagine a few former students who'd figure out mine in a heartbeat.
I know it's easy to remember, but may we change our password? I searched Help and changed the password, but it doesn't work, so I'm assuming that that ability is blocked. May we unlock that, if so? Then, if you want, we can lock it up again...