Agent Red is an agent of Prism.
More accurately would be, as mentioned in the first recorded adventure, she is one of The Agents of Prism. The capitalization appears important. What is not important, or rather, never used, are real names. Agent Red is always referred to as either that or just 'Red' and the few other agents we meet are addressed as colors as well, such as the older mentor and frequent handler, Agent Blue.
In the middle of the metropolis collectively known to the world as London, England is the actual municipality called the City of London, a square mile with its own mayor and police force and most decidedly way of doing things. Business is its primary concern. In the center of the City is the "looming glass building - a 30-story high-rise filled with unspeakable horrors, betrayed by a mere facade of joy, as workplaces often are. .. No signage broke the sophisticated lines of the building, and no external lights either. This was the headquarters of Clear Incorporated, the most secret company in the world."
If one were to take the elevator to the top floor, difficult unless one had the authorization, one could then enter another elevator which would take the rider back down and then "some inner machinery uttered a brief mechanical meshing of gears and now the elevator traveled sideways across the sky-way into the unnamed and featureless building adjacent". "If Clear Inc. was mysterious, this building was doubly so, for no regular people worked in the floors below, and what the floors contained was a mystery known only to the most senior Prismatic Agents."
Agent Red is the newest of these operatives, having just completed her training and deemed ready to go on her first mission. We are there when she meets for the first time the Prism leaders, a man and a woman, who had "bankrolled her military-grade education, plucked her from a mundane council flat, public school life and shepherded her into the Prismatic College. All without ever meeting, until today. They had given her the opportunity to reach a better life and she had not taken it for granted."
Having said that, the first words the male leader said to her irked her enough to fantasize "about leaping catlike in-between the smirking couple and silencing their judgmental stares", something she knew she could do because "two years of intense training had gifted her the ability to strangle even the most resilient target in mere moments".
Red's name comes to her pretty naturally as she is copper-haired with a fair amount of freckles about her upper torso. While she inherited her eyebrows from her Spanish father, the rest of her were all products of her Scottish mother. Obviously from the paragraph above, she also possessed a fiery temper worthy of her codename. Irked as she was in that initial meeting and sent on a mission to stop a rogue agent, she comments to Blue, "I've never killed someone before. I'm rather looking forward to it".