"My partner's here, or else I'd probably offer to do station ops or counterintrusion."

The level to which the Chief is the one calling the shots in that relationship is debatable, but her personal loyalties notwithstanding, it is entirely accurate to describe Cortana as independent. And it would be more accurate still to tack on "to a fault."

He's going to ask, so she adds: "Sierra-117."

Talking to someone else, someone not from the UNSC, she might have said "the Master Chief," but Locus is career. He'll know.