While many domain name registries are run privately quite a few country code registries (ccTLDs) have links to government. In the case of .eu, however, the registry is operated under contract to the European Commission, so it is operated on behalf of the entire European Union.
The impact of Brexit on the .eu ccTLD is something I’ve spoken about a few times in the past. The position adopted by the European Commission with respect to .eu and affected registrants has caused confusion and irritation for both registrars and registrants of .eu domain names with the uncertainty not helping.
As I noted a few months ago, the .eu policies were updated and the eligibility requirements changed. Whereas currently you need to be located in a European Union country to register a .eu domain name in the future if you are an EU citizen you will also be eligible no matter where you are in the world.
Against the backdrop of this upcoming change the European Commission issued an updated notice on the .eu domain.
So now, somehow, if you’re an EU citizen and you happen to live in the UK you’ll be able to keep your .eu domain name, but if you aren’t then you’ll lose it… probably.
The current state of play is far from ideal, though within the entire Brexit situation domains are just one tiny element.