。
After he left, she told me his name.
Literal
She [topic-は] he [subject-が] went-out-and-went [after-後で] his name [object-を] me [to-に] [told-for-me-教えてくれた].
Two stacked grammar points worth noting. 出ていった is a compound: 出る ('go out') + ~ていく (motion away from speaker's perspective), capturing the trajectory of leaving. ~た後で sets the temporal sequence ('after he had left'). And 教えてくれた marks me — the speaker — as the recipient of the kindness; without ~てくれる, it would just be neutral 'told.'