Yup, it's smaller than larger caliber (usually vehicle-mounted) rotary barrel designs, so it's 'mini'. And uses rifle caliber rounds, hence 'gun'. Put the two together and you get 'minigun'. Also, unlike its depiction in fiction, the M134 Minigun really isn't a hand-held weapon.
Although there were plans for an actual man-portable version that used 5.56mm rounds called the XM214 Microfun. But those were scrapped, because even at that even further reduced size, it was still a really unwieldy and impractical weapon.