I think, this labels and its translations are available, but I don't know where. I found nothing in the "Translate Interface" seach.
So here's my question:
is there a way to get translated month labels more elegant as like
Normally date labels (months, day, etc. in short and long version) should be translated automatically according to the language configured for Drupal interface (admin/config/regional/settings).
However, in case there might have been an issue somewhere, with Drush and the module Localization update enabled the following command forces the translation to be updated and it solved the issue in my case:
Based on GZBK's answer, I had to do following to get things right:
You can translate the month and weekname labels using the translation interface at http://example.com/admin/config/regional/translate/translate
The search is case sensitive.
To ensure that the month names or week day labels are available for translation, you can fashion a custom module such as suggested in this comment: https://drupal.org/comment/8251325#comment-8251325
Strings are only available for translation after the first time they are processed by the t() function in Drupal 7.