。
She was named chairperson.
Literal
She [topic-は] chairperson [as-に] was-designated.
指名する ('to name, designate, appoint') is the formal verb for nominating someone to a role. The に on 議長 here is the 'role-に' — marking *into what role* she was named. This usage of に shows up across change-of-state and assignment verbs: 委員に任命する ('appoint to the committee'), 部長になる ('become department head'), 代表に選ぶ ('choose as representative'). The passive 指名された frames her as the recipient of the appointment, with the appointer left implicit.