That usually isn’t a problem with CBP if the person has managed to fly to and arrive at a US airport of entry on a common carrier, even as someone with the same name as someone on the US watch lists or even the no-fly lists. It’s with the TSA that the name thing by itself is way more usually a problem, and for that the name and sex on the booking need not even be the same as that of the blacklisted figure (who may or may not even be real).

The Danish authorities do at times provide consular assistance for those Danish nationals detained for questioning even without charges having been filed.