In this (joke) ad for Midol, He-Man explains why She-Ra got the name: ‘She-Ra’, rather than the more logical-sounding: ‘She-Woman’ (seeing as how he is ‘He-Man’). So apparently what happened is that when she became She-Ra, Princess Adora got super powers, but also super painful PMS symptoms like cramping and headaches, etc. So when in this state of discomfort, Princess Adora would literally roar at people from the pain she was in, hence the name: ‘She-Ra’ (as in: “Rah!”, like a roar sound). But now that she has discovered Midol, her awful symptoms from “that time of the month” are gone, and she feels all better now. But they still call her ‘She-Ra’, just to tease her.
This is She-Ra, for those who are unfamiliar: