Usage patterns
名声を築くto build (up) one's reputation
Through years of effort, he built up his reputation in the music world.
名声が高まるfor one's fame to grow
Thanks to that invention, her fame grew.
名声を失うto lose one's good reputation
Because of the scandal, he lost his reputation overnight.
名声が広まるfor one's fame to spread
His fame spread throughout Europe.
Expressions
名声を汚すdefile one's reputation; besmirch one's name