Covid 19 is already a notifiable disease. If you have it, you are NOT allowed to withhold that fact from the authorities, howsoever it is diagnosed, for reasons of public health. So there IS no ACTUAL additional burden here!
IF you have Covid19, you do not have the right to keep this secret. That is the state of the law already as it stands! Public safety concerns take priority over your individual privacy in this specific circumstance. End of!