I feel like Claudius mostly uses her name when he wants to boss her. When he calls her by her name, he wants her to do something. In this case, it’s following Laertes. And the line he’s about to say might be interpreted as an accusation. It is, after all, Gertrude who has come in and given them enflaming news. She’s messing up his game. I feel like – if they were more in cahoots, she would not have burst in to deliver this news. If Gertrude were closely aligned with Claudius in his political workings and manipulations, she would have waited to tell Laertes about Ophelia. Is she intentionally enflaming Laertes? A Gertrude who has firmly aligned herself with Hamlet might do such a thing. I don’t think she’s aligned herself with anyone, though. She seems to just be operating on nerves by this point in the play. And now she’s the only woman left standing.