Narumi is the first to actually meet Nagi after he arrives on the island. She also saves him from drowning when he falls into the sea when going after her straw hat that was taken by the wind. Of the three maidens, Narumi is probably the one with the widest emotional range, going from a strikingly happy girl to a serious cape maiden on a moment's notice.
When the three cape maidens were asked who of them wanted to go live in solitude, Narumi was the one who offered to take on that role. (Soyogi only accepted the same because she didn't want to lose to her.) On Nagi's first visit to Narumi's little getaway, though, he learns that the place is filled with manga and plushies, which Narumi has collected while she was living there.
Narumi is a very adept swimmer, being the maiden of water, and has a talent for fishing, right up to basically swimming up to them and grabbing them right there in the sea.