Don't be fooled by the name - there's no rose in this cocktail (I really can't stand rose-flavoured anything). The name is referring to the London neighbourhood of Chelsea and the English Rose, for which Chelsea is somewhat renowned. By "English Rose," I don't mean the flower that grows on a thorny bush (which England obviously also does well) but the classic image of female English beauty - natural, pale-skinned, rosy-cheeked, dignified, and demure (but not in the modern nasty sense). English women possessing this natural beauty are still referred to as English Roses.
The ingredients in this cocktail all have English ties (gin, elderflower, English raspberries)
and the colour when mixed is the reminiscent of rosy cheeks.