。
She was named after her grandmother.
Literal
She [topic-は] grandmother [possessive-の] name [object-を] taking was-named.
命名する (めいめいする) is a formal verb meaning 'to name' or 'to christen,' and the passive ~された shows she received the naming action. 名をとる ('to take someone's name') is a set expression for naming someone after another person. This touches on the Japanese practice of choosing names with family connections — passing down readings, kanji, or name elements across generations.