Because it is not always appropriate to use someone's nickname when referring to them and I don't think it is a stretch to say a presidential debate is not a place for nicknames. There is also the question why some people get addressed with proper titles and names while others only get nicknames. When referring to fellow members of government in a setting like a debate they should be referred to in a formal manner which would normally be their title and last name not a nickname.
From your first link her complaint is she is refereed to by a nickname while others get their title and proper name.
"I wonder if Republicans understand how much they advertise their disrespect of women in debates when they consistently call women members of Congress by nicknames or first names while using titles & last names when referring to men of = stature," Ocasio-Cortez tweeted.
From your second source
AOC is a name given to me by community & the people. Y’all can call me AOC.
Government colleagues referring to each other in a public or professional context (aka who don’t know me like that) should refer to their peers as “Congresswoman,” “Representative,”etc. Basic respect 101
From your third source it is obvious he went even further by referring to some other congresswomen by referring to them as just numbers as part of a group
Trump referred to Ocasio-Cortez as “AOC plus three,” referencing her and Democratic Reps. Ilhan Omar of Minnesota, Ayanna Pressley of Massachusetts and Rashida Tlaib of Michigan, also known as “The Squad.”
It seems that Trump used the nickname because he didn't want to give her and some of her allies the same level of respect that he gives other members of congress.