Officer Lady Erin Jane Swann of the Torchwood institute, is the fake name created by Erin to move herself away from her past. Even her married name has a sense of falsity to her, Erin Jane Halliwell. 

Her real name is Erin Sturgeon, the name Jane came from her love of Jane Austen books and the last name Swann always sounded like a woman in a fairytale, which at the time of creating her new name, she needed. The title of Lady however, was awarded to her by Queen Victoria after their time spent together at the Torchwood Estate. 

Christopher Halliwell is the name of Erin Swann's fiance, he's a doctor working at St Mary's hospital and is anything but oblivious to his partners extreme seeming work issues. 

He's American and has lived in the UK for many years after inheriting a manor from his grandmother, which is now where he and Erin live.