Uunartoq Qeqertaq – translated from Inuit as Warming Island – joins Southern Sudan and nearly 7,000 other countries and places added or changed since the last edition of the Times Comprehensive Atlas of the World.
The Greenland ice sheet is said to have shrunk by about 15% in 20 years. Update 19 Sep: the 15% figure is said to be an exaggeration.  (See This is what global warming looks like.) Where, exactly things go from here, and when, is hard to predict. The ice sheet may not disappear as quickly as some previous models have suggested. (The precise impacts of fresh and seawater ice melting are also unpredictable.)
But in the absence of dramatic changes in the nature and pattern of human activity, the likely trend is towards complete disappearance of the ice sheet. In a review of Deep Future: The Next 100,000 Years of Life on Earth by Curt Stager, Scott L. Wing writes:
Relying on simulations of the effects of high partial pressure of carbon dioxide by Richard Alley, Jeff Ridley, and others, Stager lays out the development of Greenland's landscape and economy as its ice cap melts. He even playfully proposes a name, Ny Fjord (New Fjord), for the giant tongue of ocean that could come to occupy central Greenland by 5000 CE. He envisions a thriving Arctic-fishing industry lining the shores of the 400-m-deep fjord, then explains how the fjord would (to the shock of most nongeologists) empty over the succeeding 50,000 years as isostatic rebound following deglaciation raises the crust of central Greenland.
 (added 21 Sep): see Greenland Meltdown at Realclimate.