They don't, really. At least in Germany, the "right to one's likeness" already exists as an explicit law but entirely separate from copyright and trademark law, which is what governs brand likeness.

What Denmark is proposing is simply an extension of the existing safeguards that many EU countries, as well as EU legislation generally, already provide regarding the control of their citizens over their likeness. It is not really revolutionary but a sensible addition in the light of technological advancements.