In the case of Derry/Londonderry, as discussed in the previously linked wikipedia article, it varies - depending on when the sign was put up, who put up the sign, and what aspect of the place the sign was about (e.g. council, airport, something else).
In the case of Dingle/An Daingean, the dispute was twofold - it’s officially in a Gaeltacht so names should be Irish only, but some people locally are keen for the well-known-to-tourists English name “Dingle” to also appear; and also as I understand it** the locally preferred Irish name was An Daingean rather than Daingean Uí Chúis.
That’s why it’s useful to have a name that is a “genuine multilingual name” for use by people when people really do use that as a name (people really might use the name “Dingle An Daingean” in speech). It’s only possible to do this if people don’t use name as a dumping ground for “all possible names”. As an example of that, https://www.openstreetmap.org/node/21395759/history is called Aberteifi in one language and Cardigan in another; I’ve never heard it called both as one name*** - but if you look here you’ll see I’ve avoided that errant slash.
Given the worldwide usage of “name” as “all possible names stuffed into one field” as opposed to genuine bilingual names I suspect that there’s no longer any chance to have “name” as the field for “genuine multilingual names”; maybe we need another one?
** this was mostly from speaking to people in pubs. It was not a representative survey 
*** A search for both words finds lot of articles where both proper names appear, but none as part of one single name.