How can my health insurance company change my address with out my consent?

If your health insurance is through your employer, the insurance company will accept changes of address from your employer.

Also, if they have mailed you something that was returned as undeliverable and the post office indicated a forwarding address on the returned mail, then the insurance company would update their records accordingly.

Those are just 2 examples. But there are a handful of ways that the insurance company can legitimately change your address on record without it being directly reported by you. (Also, if someone else who is currently on your policy called to report an address change, they would accept that too.)

However, if you feel that your address was changed w/them fraudulently and not for one of those handful of valid circumstances, definitely follow up with your insurance company. They certainly want to make sure that they have your correct address on file...due to HIPAA privacy laws, they don't want to be sending potentially confidential information to the wrong address.

When someone calls the insurer to change the address, they ask them security questions to verify that person's identity. Is there anyone who would have reason to want to impersonate you and change your address for some reason? (You hate to think of that sort of thing happening, but its not outside the realm of possibility.)

The insurance company shouldn't be making changes without your knowledge, however:

By law you should have provided them with your most current address, however, there is nothing unlawful about keeping on file information that is public information.

You can always ask for a copy of all the information they have on you, by law they have to provide it to you.

ANY Insurance company cannot make ANY changes to your personal information without first notifying you. You have the right to accept or refuse any changes.
If they are also making changes to the coverage in a policy, they must also notify you.
If this is a private health insurance, let them know, by certified mail, that their information is now incorrect. Give them the correct address.
If this is a company health insurance policy, Notify your HR about it immediately.

When your address changes without your consent, it is either a clerical error, or someone is hijacking your identity.

Someone may be setting up an identity at a different address so that you will not get any mail on your 'redirected identity'.
They will then use your new address to open up credit accounts, even mortgage your home, sell it.

Do not be content to get a clerical error fixed. Do a thorough check on your credit status and set up a sting with police if needed.

They can't just randomly change your address, so unless someone else called purporting to be you and somehow had enough information to convince them they are you, how would it have changed?

What do you mean they "changed your address"? If your address in their records in wrong, just have them correct it.

The only way they can change it, is if their agent notifies them of your new address, or they mailed something to you, and the post office notified them of your new address - or, if you notified them, on the payment slip.