 Upon being designated , Tropical Depression Fifteen developed deep convection close to , and to the east of , the center of circulation . At the same time , banding features became better organized . Later on September 5 , the overall cloud pattern improved while thunderstorm activity condensed and deepened within the increasingly well @-@ defined circulation . Just six hours after being designated as a tropical depression , the cyclone intensified into a tropical storm ; it was given the name Nate by the National Hurricane Center . Over the following two days , Nate drifted slowly northeastward towards Bermuda . 
