From the link:

Dick Carter, Chair of the Delaware Heritage Commission, states that the name of Murderkill River is taken from the original Dutch for Mother River. Mother is moeder in Middle Dutch, and river is Kille. Later, under British rule, the word "River" was added to the waterway's name, effectively making it "mother river river."

The term "kill" is used in areas of Dutch influence in the Netherlands' former North American colony of New Netherland, primarily the Hudson and Delaware Valleys to describe a creek, river, tidal inlet, strait, or arm of the, sea such as Bronx Kill in New York and Schuylkill River in Pennsylvania.

Delaware's creeks and rivers are slow-moving and there is deep mud associated with marshy rivers. Dutch "modder" = mud, a false cognate to "mother." Modder Kill = Muddy Creek or Muddy River. The word is still used in Dutch, such as this Dutch video of a tractor stuck in mud ("vast in de modder").[12]