The dynamic would shift in multiple ways. Hermione would be seen as part of the Hogwarts 'royalty' in a sense. This could make some students jealous, but also make others want to befriend her more. In terms of the professors, they would likely have higher expectations of her, not just because she's Hermione, but because she represents the McGonagall family. McGonagall would be more likely to defend Hermione in any disputes with other students or faculty. And Hermione would have to deal with the added pressure of living up to the McGonagall name in the wizarding world.
It would change a great deal. First off, McGonagall would probably be more involved in Hermione's academic progress on a personal level. She might give her special assignments or extra tutoring. As for the other professors, they might view Hermione as having an 'inside track'. For instance, Professor Flitwick could be more lenient with her in Charms class. This new dynamic would add a whole new layer to Hermione's Hogwarts experience and how she interacts with the faculty.
Chapter 822, "The Yu Family Gave Too Much", is the clearest early answer because it turns Yu's situation into a concrete plot event. It opens with Jiang Li entered the reception hall, which was already quite crowded.
Chapter 600, "You merchants aren't even fit to carry my shoes!", is the clearest early answer because it turns Shang Zhenhe's situation into a concrete plot event. It opens with Shen Ruobing was not deaf to the ironic tone in Jin Siyue's comments,...
Chapter 625, "An Anonymous Corpse Found in the Wilderness?!", is the clearest early answer because it turns Jiang Cheng's situation into a concrete plot event.
Chapter 604, "Shiguang, originally named Shen Guang", is the clearest early answer because it turns Jiang Shixu's situation into a concrete plot event. The chapter gives readers a real answer by opening on Fortunately, the other person did not recognize him; they just stared...
Chapter 885, "Isn't This Wine?", is the clearest early answer because it turns Seeing Shuiyun's situation into a concrete plot event. A useful checkpoint is the way the scene starts with Daoist Shuiyun's words weighed heavily on Jiang Li's heart like a...
Chapter 656, "If he's the grandson of the richest man, then I am the richest man!", is the clearest early answer because it turns Tang Yao's situation into a concrete plot event. Early on, But if she knew he was still unchanged, or even worse than before,....
The best chapter pointer here is Chapter 2, "What Kind of In-laws Are They?". It opens with On the top floor of the Financial Building, a gathering of dark clouds... and closes on Jiang, Lin Manru, turned pale and quickly explained, "It's not eloping, my....
Chapter 466, "Are There Really Wild Boars?!", is the clearest early answer because it turns Zheng Xun's situation into a concrete plot event. The chapter turns that into something concrete by moving from The lady sure acts like a lady, even in 'Wilderness Survival' she...
Chapter 523, "Are the Researchers Sweating Profusely Now?", is the clearest early answer because it turns Gu Yu's situation into a concrete plot event. It opens with This is supposed to be a life-saving 'peace charm' tailored for the...
Chapter 570, "A Simple Auto-Attack Baits Out an Ultimate from the Enemy", is the clearest early answer because the buildup finally cashes out in a real clash. The chapter turns that into something concrete by moving from What the heck is that?" "?? to It was impossible for Jiang Li not to know;