I always think of it as 'Londonderry', the 'Londonderry Air' was a tune I grew up with. A lot of us have long memories. Prince Charles probably remembers Lord Mountbatten very well and considers his death as murder, but I'm certain he would shake hands with the mayor in the interests of present peace.
I have known it called Derry since the time of the troubles when London and the English were dirty words. Either call it Derry or Londonderry but don't mix it up in the same article (ref my original post).
As a matter of fact mixing it up is a perfect solution to the conundrum. The BBC have traditionally done that for example in some of their nees reports in an effort to appease each side. Both names are generally accepted as ‘correct’
Brexit won't force border control. The EU and Eire might, but that would be of their own deliberate choosing. The EU may choose to be awkward for the heck of it, and Eire may decide it would prefer border control to telling the EU to keep it's nose out of their business, and their arrangements with other nations.
I've worked and lived in mining areas for years and even now after all the years that have passed since '84 the the feeling of us or them is still there even if it is usually hidden it never goes away and the bitterness still lingers.One guy who used to be a very good friend spent a year on the picket lines and gave me a lot of personal abuse even though my union was not strike and he still can't understand while I don't talk to him.I know it's not the same as the troubles in Ireland but some things people NEVER forget which ever side they support.
Legally, the city and county are both called Londonderry still and the only time I would ever use "Derry" is in connexion with the Apprentice Boys of Derry.
The late, great Gerry Anderson coined the name "Stroke City" and would constantly (and ironically) call his hometown "Derry/Londonderry. My dad was a staunch unionist but always referred to it as "Derry" (even though he would probably have argued that "Londonderry" was the "proper" name (!). I have never heard either cathedral there ever called anything other than "Derry Cathedral" Officially the City council name is also "Derry".