It most likely depends on whether or not the business operates in Denmark or not. Not sure how individual data laws will play with EU law but for sure you can still use the deepfakes on WeChat in China
This kind of reframing of the words (by Denmark, not you) has led in the past to the abuse of what something is called to reshape slavery in modern times.
On the surface, this seems like a great idea: give the people autonomy on their likeness and its use.
What if you're in debt? Sell your likeness? Should companies be allowed to lure ppl with commercials about making money by selling their likeness? Should we create laws about extortion and coercion that include forcibly making someone give up their likeness? Short-term likeness "rental farms"? What if the terms of the likeness are a different financial mechanism like a reverse mortgage or a lease? International laws agree on all these terms?
We also collectively determined that slavery is illegal, but it still happens by exactly manipulating the mechanisms to get at the resource: come work in the Arab Emirates. Come to Canada, send money back to your family. If you pay me $5k, I will get you out of this hellhole to a country where you can have a job, money, freedom... But you have to spend 6 weeks in a shipping container and give us 6 months of work when you get there.
The only way to make a person's likeness an inviolable right is to make it an inviolable right... With no monetary value.