In general, entities are stored in the intended language/script of the primary market, but this may not be Latin script.  Some users then incorrectly place a Latin script transl(iter)ation in the Disambiguation field so they can see it on the website.  (It isn't helpful for search because aliases and pseudo-releases already take care of that.)

Ideally, I think the server/UI should offer an option to show the appropriate Alias in parentheses next to the primary name of the Entity.  This could hinge off the existing website language option, but the available languages would be more limited than the available alias languages.

Artist in-line search already does something like this, but this would be helpful for general display of entities like Release Groups, Releases, and Labels.  (It could also serve a function on Recordings on a Medium, but most transliterations are stored in Pseudo-release track titles rather than in Recording Aliases.)