Have you checked first that tattoos do not affect organ donation eligibility, or have any legal/medical weight whatsoever compared to, say, an organ donor card or check on your driver's license?
It would be worth double-checking your local regulations, but tattoos do not generally restrict you from organ donation. You should make sure you get your tattoo from a licensed business, of course.
As far as legal status -- that is a good question. I would think that as long as you updated it at least as often as you update your driver's licence, it would remain a valid indicator of your intent. That might mean adding a date to the tattoo, and adding another one every few years. You might contact your local hospital and see what they would do if they had a fresh corpse with no ID but a organ donor tattoo...
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