、。
I need her name to make a reservation.
Literal
Reservation [object-を] do-[for-には], her-of name [subject-が] needed is.
~には is a composite: the purpose-marker に plus topic-marker は, meaning 'in order to X' as a framed topic. The predicate 必要だ takes が for the thing that is needed — 'X ga hitsuyou da' rather than 'X wo hitsuyou to suru.' Note how Japanese uses が where English would say 'I need': the needed thing is the grammatical subject.