Is there an organism which has a common English name which overlaps with another organism's scientific name (or vice versa?)
One great example I know of is the duck-billed platypus (Ornithorhynchus anatinus),  often simply called a platypus, which shares its name with the Platypus genus of ambrosia beetle. 

Wikipedia gives a brief history of the taxonomy of the duck-billed platypus:


  The common name "platypus" is the latinisation of the Greek word πλατύπους (platupous), "flat-footed", from πλατύς (platus), "broad, wide, flat" and πούς (pous), "foot". Shaw assigned it as a Linnaean genus name when he initially described it, but the term was quickly discovered to belong already to the wood-boring ambrosia beetle genus Platypus. It was independently described as Ornithorhynchus paradoxus by Johann Blumenbach in 1800 (from a specimen given to him by Sir Joseph Banks) and following the rules of priority of nomenclature, it was later officially recognised as Ornithorhynchus anatinus. The scientific name Ornithorhynchus anatinus is derived from ορνιθόρυνχος (ornithorhynkhos), which literally means "bird snout" in Greek; and anatinus, which means "duck-like" in Latin.