The TUNE is called the Londonderry Air (because the first person to note it called it that) - we've (little or) no idea what anyone called it before then. The CITY is variously called Derry/Londonderry or Stroke City (or even Doire Cholmchoille, más mian leat). The SONG is called "Danny Boy" because that's the only set of (many) words that, for better or worse, has caught on. As for me, I prefer "Maidin i mBéara", written by a Protesant Gael - but probably only because I learned that set when very young.

Regards
p.s. And, of course, the only thing that should be banned in pubs before (or after) closing time is obnoxious singing - of ANY song!