That's her full name, give me guff about it if you want, but she's from a time and world where only the rich or powerful have last names.
Aine's only had one serious relationship in her life, a guy named Curtis. After their training as fighters they took a job as part of a security detail on merchant caravans. Not the same one, and when the time of their contract ended, Curtis didn't return. Aine went off to find her own fortune, and could be labeled as a loose woman, or would be if she wasn't discerning in whom she slept with. Plus being the odd woman in a male dominated career, Aine often pushes for equal treatment for herself, which I believe other swordsmen are willing to give after seeing her skill with the claymore. Employers often aren't so kind, which often doesn't mix well with Aine's blunt nature. (If you want, I'll show you an amusing interaction between her and an employer.)
Now, Aine often doesn't have relationships beyond one night stands or flings. Part of this is she fears the loss of her identity that marriage brings in her mind. She would no longer be Aine, daughter of Cormac but Aine, wife of (guy's name), and this terrifies her. Please do note that names often do hold power, to be able to name something was to gain power over it, and names where often changed to signify a major change in the person. I do find it interesting that the loss of her identity scares her when she does often have to risk life and limb in her job.