"mukuro-sama.."
Chrome's relationship to Mukuro is interesting. Out of all the dying girls in the world he could have chosen, he chooses this weak and useless little girl as his host body. She doesn't even have all her organs in tact! There was something special about this girl that only Mukuro could see - and is Chrome ever greatful for getting the chance at another life. It's easy to see how much she respects him by the way she says his name and adds an appropriate suffix: "Mukuro-sama" The suffix -sama can be translated into "master".
Let's remember that Nagi was a girl that was useless to her world, not even her parents had sympathy for her death. She was not clearly understood by many people, and did not have any known friends. When Mukuro told Nagi that he needed her - those were words that have never been said to her before. This girl, as useless as she knows herself to be, was needed by a complete stranger. She didn't know what was going on when she took Mukuro's hand, but I think that the wonder and awe of that moment made her go for it.
In return for making her feel like she was beneficial for someone else, she gives her everything to Mukuro. I think this is the main reason why she's so attached to him and addresses him by "Mukuro-sama" ... out of being thankful to him.
