Per T263294#6487346. In the mobile web version of Wikipedia (*.m.wikipedia.org), the language name for the Norwegian Bokmål Wikipdia is listed as "norsk" when it should be "norsk bokmål". This was fixed for desktop back in November with the addition of the $wgInterlanguageLinkCodeMap in InitialiseSettings.php, but apparently mobile web doesn't recognize this setting. Ideally it would, so this doesn't have to be fixed in multiple places.
In summary, no should display the name for nb, but only for Wikipedia, not other Wikimedia projects.