Yeah I always thought that not using honorifics like san/kun/chan meant that you were closer to that person. She only ever called him Naruto.
This is the confusing part because I have heard it both ways. It can either be that the person is close or they wanted to insult the person by not using honorifics. I guess it depends on the situation.
However, we can prove that Sakura does it out of caring and closeness to Naruto by one simple thing...Sai. Sai actually asks about it and mentions that they are close and why Sakura doesn't use honorifics. I don't think this scene was just a coincidence and since Sai basically plays what we call "The straight man" it would make sense.
For those who don't know, the "Straight man" in stories is not sexual orientation, but rather the emphasis that the person is meant to set up something. They are usually more for compedy, but I feel they can set up anything. They are the outsider looking in pointing out the obvious. I believe Sai was supposed to be the Straight man to NS getting together because we knew Naruto and Sakura weren't doing it on their own due to their personalities in conflict of wanting to make the other happy and thinking they themselves cannot make the other happy which is the opposite. If this was Sai's original intention, then it would make sense for all the scenes with him setting up NS or pushing a NS narrative like th confession scene.