[johannes1234321]

Depends on the identity goin forward. If England+Wales stick to the name for some reason they will continue using it, and Scots and NI get new ones. (Well, later not if they merge with Republic of Ireland) If they form a new country and rename to "England" (poor Welsh) or "South Britain" they likely will be legal successor of treaties and stuff (like Russia being legal successor of USSR) and can use .UK for the time being.

One effect can be seen on .eu: After Brexit UK entities aren't eligible for .eu domains anymore and depending on the outcome on Oct 31st might lose it immediately (while there are statements for a grace period even on Brexit without further agreement ... but no deal leads to no legal requirement)