Staff using POCT Supplies for Self Testing

I have a disclaimer that I have every user sign or initial during their observed competency that they acknowledge that they cannot perform self testing and all testing performed with their credentials will be their responsibility. 

Always a battle.  Often all you can really do is make it 'harder' and make it not worth the trouble to try it.  For example, if it's device-based and requires a patient ID, lockout manual patient ID entries and set scanned entries to match only the character limit of your valid patient ID.  If you allow an "emergency ID" for actual patients, and that is what is being used by employees to self-test, ensure you have a contact on the unit that is aware and can follow up when that's being abused.  Manual tests are of course much harder to track, unless you're doing a supply count regularly.  One option for that - locking up supplies, especially on off-shifts.  We had to do that at a few locations in our health system when people were crazy for COVID Ag tests and couldn't find them in the store.  You do what you have to do...

What a good question!
Since none of the reagents/kits come out of the lab budget, it's really 'on' the testing site to patrol self-testing or coworker testing (where I work). 
Since I'm the one who sees the unsolicited tests come through middleware (patient ID gets flagged which pulls it out of crossing into EMR), I chase each of those down. Paraphrasing - I email each operator on record for having performed the test, and state something like: 'if this is a real patient test', here are the steps to take to ensure the patient result gets into the EMR chart.
If this 'patient ID' was for training purposes/demo, or it's your specimen or that of a coworker, then please be advised your supervisor is cc'd on this email. Thank you". ;-)

go get 'em Peggy!  :)

Our system created a Glucometer Test with Emergent ID - ID Card Not Completed" event in the IRIS-PX tracking system so the unit manager gets to follow-up on those. When entering the IRIS, I also email the operator, unit manager, and educator with the issue and IRIS event #. It's been very illuminating and has helped us create some work aids for staff. On floors where the patient should have an armband on, they are also instructed to scan the armband rather than enter an emergent ID so we can track armband issues. For some reason, they think if the meter displays, "Not a valid Patient ID", entering all 9's or 0's resolves the issue (and they don't send an ID card).

Manual testing is it's own nightmare and I'm just counting on the managers and ANMs.

We don't call it out as that lets even consider the possibility.  Our policy states that testing can be performed only on hospital-registered patients.