“Right” side is ALWAYS given nicknames. Including being used in “news” organizations.
Meanwhile, you’ll rarely see “left-wing”, nor will you ever see any nicknames come up for them in official news.
There is ‘Far-Right’, but no ‘Far-Left’.
There are ‘Right-Wing Hate Groups’, but no ‘Left-Wing Hate Groups’.
There are ‘Right-Wing Domestic Terrorists’, but no ‘Left-Wing Domestic Terrorists’...................