According to John Man^1 it was called this as Genghis's family was known as the 'Golden Clan', and the Mongolian word ord/orde meant a palace, or for the Mongols a tent. Hence Batu's (initial leader of the khanate) apparent use of a gold coloured tent as his 'palace', and the shift of ord/orde to horde led to the khanate being called the Golden Horde.

Worth noting that initially it was known as the Khanate of Qipchak^2 (named after the nomads who previously inhabited that area) and according to David Morgan the popularization of Golden Horde came about later.

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^1: The Mongol Empire, John Man

^2: David Morgan, The Mongols