In Premier, your CS Rating stays hidden until you have won ten matches in the current season. It is ten wins, not ten games, so a run of losses simply means more matches before the number appears. Once it is revealed, the rating is public: teammates, opponents and the leaderboards see it from your very next match.
The rating you receive depends on more than the plain win count. Every result moves it, and the change is larger or smaller depending on the rating of the opponents you faced. A loss against a strong lobby costs less than a loss against weaker players, and a win against a strong team is worth the most.
The number then lands in one of the colour bands everyone recognises: grey below 5,000, light blue from 5,000, blue from 10,000, purple from 15,000, pink from 20,000, red from 25,000 and gold from 30,000. Players care about the colour first, because it is what appears next to their name in every lobby. A good placement run aims to land you as high on that ladder as your matches allow, rather than just getting the ten wins over with.