。
She made a name for herself as a singer.
Literal
She [topic-は] singer [as-として] name [object-を] raised.
名を挙げる ('lift up one's name') is the set phrase for gaining fame, making a name for oneself, or distinguishing oneself in a field. The kanji 挙 is the same one used in 挙手 ('raising one's hand') and 選挙 ('election') — the underlying image is something being raised up for others to see. Compared with simply becoming 有名 ('famous'), 名を挙げる carries a sense of active achievement, not just recognition. A natural fit for biographical writing.