There are plenty of synonyms for the phrase "make a name for yourself." You could say "build a reputation," "forge a path," "establish yourself," "get known," "gain recognition," "make an impression," "carve out a niche," or "make your mark." Each of these phrases carries a slightly different connotation, but they all express the idea of making a significant impact in your field or industry. Whether you're looking to become a well-known musician, a respected author, a successful entrepreneur, or a sought-after expert in your field, finding new ways to "make a name for yourself" is essential to your success.