"won renown" is correct and usable in written English.
You can use it when you want to refer to someone who has achieved something notable, either by their own actions or because of their reputation in their field. For example: "He won renown as a talented actor after his remarkable performance in the play."
Saint-Gaudens won renown with consummate portrait busts.
This is the genre where he first won renown.
Its features on residential architecture, fine arts, and domestic life won renown.
A man of wide culture, he also won renown as a conductor and lecturer.
Both won renown while working at the leftist New Statesman in the 1970's.
Andrew Jackson won renown for his victory over the British in the Battle of New Orleans.
Tycho wins renown by identifying new stars, including a supernova, but after his royal patron dies, Tycho finds himself out of favor with the son and successor, Christian IV.
The hero, he believed, is one who is impelled by strong passions to win renown through the performance of great deeds preferably (but not necessarily) those contributing to the well-being of humanity.
Charles W. Bailey, who edited The Minneapolis Tribune for most of the 1970s, when it was among the most polished of the nation's midsize daily newspapers, after earlier winning renown as a co-author of the best-selling cold war novel "Seven Days in May," died on Tuesday in Englewood, N.J.
This event closed the first period of his life, during which he was, on his own admission, "a man given to the vanities of the world, whose chief delight consisted in martial exercises, with a great and vain desire to win renown" (Autobiography, 1).
And she argues that the story of Lee Miller -- who began as Man Ray's model and assistant and went on to win renown of her own as a photographer during World War II -- shows that a talented muse can sometimes make the difficult transition to becoming an artist.
