I have just read three different explanations of the name Generalife. The original of the name Generalife could be large garden, high garden of paradise or garden of the architect. It is quite normal for scholars to disagree about the origin of names in Granada. When the Christians overtook Granada in 1492 they changed many of the place names to sound more like the Spanish they spoke at the time but the place names were not changed completely. To find the original Arabic the scholars have to trace back the sound of the modern Spanish name to the original Arabic name. So it is like a form of Chinese whispers dependent on a good knowledge of very old Arabic and Spanish. For this reason it is not surprising that you will read many differing explanations of the names of places in Granada.