。
She was named Alice after her aunt.
Literal
She [topic-は] aunt [of-の] name [object-を] taking Alice [as-と] was-named.
名をとって (taking the name of) explains the origin of the naming — the aunt's name served as the source. アリスと名づけられた uses the quotative と to mark the name given, plus the passive of 名づける (to name) — she was named, not she named herself. This pattern of naming children after relatives is common across cultures; the Japanese expression 名をとる (to take someone's name) specifically means borrowing from an existing name.