Why the name 中元节 for hungry ghost festival?
Baidu:

中元节  ...而被称为“中元节”，则是源于东汉后道教的说法。道教有“三元说”，“天官上元赐福，地官中元赦罪，水官下元解厄，“中元”之名由此而来...


三元说 ...正月十五日为上元节，七月十五日为中元节，十月十五日为下元节...

地官中元赦罪 = Underworld officer grants amnesty on 15th July
Ghosts in hell are basically prisoners in jail, on 15th July every year, they are allowed to leave the underworld and visit their family in the world of the living
Other names for 中元节 are 七月半、七月十四、祭祖节、盂兰盆节、地官节 are all based on this story
It is called 鬼节 because it is a festival for the ghosts, not hungry ghosts (饿鬼). 饿鬼 were the most sinful people before they died, and they are never allowed to leave the hungry ghost hell