。
My father named me after my aunt.
Literal
Father [topic-は] aunt's name [object-を] taking my name [into-に] did [polite-ました].
名前をとって~の名前にする literally means 'took the name and made it my name.' This is how Japanese expresses 'named after someone.' 叔母さん is 'aunt' (father's or mother's younger sister).