pls advise if one should translate the award name ? e.g. we have Russian award called REDCOLLEGIA, and in English this word means "the editorial board". Is it correct if I say "they have won "Redcollegia" ( the editorial board) award for this investigation."
You can add it in parentheses (), you can add the translation in a footnote or you can leave it in the original form if you prefer. If adding parentheses, try "Redcollegia award (the editorial board award)", not "Redcollegia (the editorial board) award". The latter looks messy.
In case of doubts, consult google, see whether there exist English texts with this name translated. In case of very official/important texts, the proper course of action is to consult your ministry of education as they are responsible for knowing proper translation. Usually people only do so when translating their university titles (while applying for a job/studies abroad), as PhD in RU will mean a wildly different thing than PhD in the USA etc.