"May I call you Rin?" A tentativeness is evident, wary of implying he should go by the moniker most humans have gravitated towards. "Unless you prefer SecUnit? Or something else?"

She's more than happy to address him by whatever name suits him. Names are important. Although a whole series of androids share hers, she was the first Chloe. The name has a meaning, and it was chosen for her.

Murderbot is a pretty metal name. It might raise an android eyebrow. Then again, humans have come up with all sorts of... creative ways to brand androids so it doesn't mean she'd assume it's literal and accurate.