This is the most common spelling of this name in the United Kingdom, Australia and New Zealand; in the United States the spellings Haley and Hailey are more popular.
In Britain the parallel form Alice, derived via Old French, has historically been more common than Adelaide, though this form did gain some currency in the 19th century due to the popularity of the German-born wife of King William IV, for whom the city of Adelaide in Australia was named in 1836.