Apparently, the Amstel's name is derived from Aeme stelle, old Dutch for 'area abounding with water'. The Amstel starts just south of Uithoorn and ends at Amsterdam where it used to meet the IJ. However, in 1936 the last part of the river (the Rokin) was filled in, so the river now ends at Spui square, although it remains connected to the IJ through subterraneous pipes.
Amsterdam took its name from the river. The city developed out of a small fishing village called Amstelredam, built in the 13th century alongside a dam at the mouth of the river.
wikipedia has loads more