She called him out by name.

Literal

She [topic-は] him [object-を] naming [by-で] called.

名指し (なざし) is a noun meaning 'naming, calling out by name' — combined with instrumental で it becomes the adverbial 名指しで, 'by name (specifically),' often with the undertone of singling someone out, calling them out rather than referring to them vaguely. Plain 呼ぶ usually means 'to call (out to), summon,' but with 名指しで the meaning shifts toward 'name openly, single out' — used especially when someone is publicly or pointedly identified, such as in accusations or denunciations.