'built a name' is a correct and usable phrase in written English.
You can use it when you want to describe someone or something that has become well-known or successful. For example, "He built a name for himself over the years as one of the best doctors in the country."
She started Crème Delicious a year ago and has quickly built a name for herself for her minute henna masterpieces.
So we built a name and a good reputation.
The company's bridal business, started in 2004, first built a name on plentiful color options and several silhouettes to ensure the wedding party matched.
Media savvy, Bo had built a name for himself promoting the "Chongqing model," a leftist-populist mixture of strong state, Maoist paeans ("Red songs"), crackdown on crime, equality over productivity and redistribution of wealth.
Although colored diamonds are extremely rare, the jeweler Lev Leviev has built a name selling some of the biggest in the world since opening his first Leviev store, in London, in 2006.
She has subsequently built a name as a comic actress in Hollywood, appearing in films such as Wedding Crashers and Confessions of a Shopaholic and plays Myrtle Wilson in Baz Luhrmann's recent big screen adaptation of The Great Gatsby.
For a time anyone trying to build a name in the scene had to turn their hand to Amen.
So he stumped every working day for almost 25 years to build a name for himself.On August 30th it paid off.
You want to build a name for yourself and your families.' I stand up all the time and say this.
Season after season the French designer Anne Valérie Hash continues to build a name for herself as the creator of clothing in modern silhouettes but with a feminine side.
But as it tries to build a name in the United States, the London-based joint venture has not carried the Sony brand name across the ocean until now.
