make a name for oneself

make a name for oneself (to become famous or respected by a lot of people, create a good reputation) — заслужить себе хорошую репутацию; сделать себе имя

Example 1: My brother has made a name for himself as one of the best lawyers in the city.
Example 2: At the beginning of his junior year, he discovered a passion for filmmaking and made a name for himself among friends and teachers with his storytelling in videos made with digital cameras and editing software. (nytimes.com)

See also
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[win one's spurs]