HDL was called good cholesterol because:

HDL Good and Bad cholesterol terminology was used earlier. Now these terms 'good' & 'bad' cholesterol are discarded. HDL was called good cholesterol because of reverse cholesterol transpo i.e. it takes cholesterol from peripheral tissue to liver. HDL conves this cholesterol into cholesterol ester with the help of enzyme LCAT-Lecithin Cholesterol Acyl Transferase. This enzyme transfers fatty acid from lecithin (a phospholipid) to cholesterol. Lecithin after losing fatty acid becomes lysolecithin (See fig below).