。
She refused to give her name.
Literal
She [topic-は] name [object-を] say [subject-を] disliked.
名前を言うのを嫌がった — 嫌がる (いやがる, 'to show reluctance') is the ~がる form of 嫌 ('disliked'). Required here because we're describing a third person's feelings.
。
She refused to give her name.