Loveday is an agent with the Ivory Tower.
The lack of a last name comes from the fact that Loveday is really a codename. It was given her by herself out of a book her mother left her years before. Loveday tells us that only a couple of her closest associates know the name on her birth certificate and she aims to keep it that way.
A blurb for the first recorded adventure tells us a good deal more about her with: "Known only to the CIA and her handler father, Loveday aspires to be the greatest teenage spy who ever lived. In a hidden bunker under a swanky hotel, she and her team train and execute missions without being noticed by the outside world."
She lets us know in the opening segment of that initial adventure as she infiltrates a private jet, tranquilizes the handful of passengers, steals a valuable briefcase, and then forces to pilot to descend to breathable altitude so she can parachute out that her role model for this was the infamous D.B. Cooper. She also tells us that he was really a retired CIA agent stealing something from a passenger on that airliner. "The ransom and escape in midair were just theatrics. My grandpa was a dramatic person." Loveday is pretty dramatic herself when she lets herself be.
Soon we learn that her father, codename (we assume) Royal, is head of the Ivory Tower team, that term apparently a reference to the very interesting headquarters of the small group directly connected to the Agency but also largely autonomous of its control. [Note, on that HQ, it is neither a tower nor made to look the bit ivory.] He has helped train her to be potentially be the best agent the CIA has ever had but she is still 17 and still learning and still capable of making mistakes.