First thing, you need to add an INI token to LabVIEW.ini file, so you can display Unicode in LabVIEW.
https://knowledge.ni.com/KnowledgeArticleDetails?id=kA00Z000000kJRNSA2&l=en-CA
That allows to at least display the characters when copied on the front panel or block diagram (instead of showing up as a "?"). However it does not work with the caption text unless your OS environment supports the language pack. As you can see below, my OS has French and English installed, but not Chinese or Cyrillic characters. I can display the unicodes when I paste directly from a source, so you can try it on a virtual machine with the proper regional settings, and that should work.
** Edit: there is probably another step missing, because I can't get it to show up on my VM with a Russian keyboard installed...
** Edit #2: OK, it works. Turns out that the cyrillic character I had copied from google was not part of the Russian keyboard. I have no way to tell :-). But now it works with another character generated from the russian keyboard itself: "ф".