Rather than demonstrating Peggy's ruthlessness, I viewed her calling Don by his first name as a recognition that they were now on equal footing, obviously not with respect to positions on the totem pole, but in the greater sense of their mutual respect and, more importantly, trust of each other. Don respects that Peggy has shown initiative in the past and has rewarded her. She's proven time and again that she's earned it.
Also, he had just chided her for being late with her assignment in front of the others, even though he knew she had been taking care of his girlfriend and sacrificing sleep. The "Don" moment, to me, was a reinforcement of what she had said in the police station earlier in the episode, something about not treating her badly because she might remind him of his misstep.
The episode set up a certain parallel between Bobbie and Don, with Bobbie clearly representing the female version of Don. Bobbie climbed the ranks, escaped an abusive past and has clearly reinvented herself as a Hollywood power player. The difference is, unlike Bobbie, who is all about about negotiation and doesn't do anything without some sort of bargaining chip in mind, Don sought Peggy out at her lowest point in life for no other reason than that he cares for her on a different level than any other female in his life. It was also on the tails of learning his brother had committed suicide, so I think he was especially concerned about letting another person in his life succomb to a similar fate. Peggy seems to be the one person in the office in which Don sees himself most reflected.
"The mantle of spinsterhood was definitely in her shoulders. She was twenty five and looked it."
-Gone With the Wind by Margaret Mitchell