。
She checked the list to see whether her name was on it.
Literal
She [topic-は] her own name [subject-が] exists [whether-or-not-かどうか] roster [object-を] examined.
~かどうか makes the embedded question explicit — 'whether or not X.' Standard grammar for embedding yes-no questions inside a larger clause; the か alone (without どうか) is also possible but feels slightly less spelled-out. 調べる ('to investigate, examine, check') is a more deliberate verb than 目を通す ('skim'): she actively searched the list, not just glanced at it.