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.
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.
A practical answer is Chapter 10, because it turns the idea into a concrete scene. The chapter opens with Qiao's shocked face struggle to recover, Lin Manru also tasted for the..., adds pressure through The young man stood motionless, his gaze fixed on the girl below, and..., and ends on Who was.
Chapter 751, "Even if both perish, he must pay the price!", is the clearest early answer because it turns Shu Yan's situation into a concrete plot event. Early on, She cried out for heaven and earth, but her beloved was just.... By the end, Why did they have to take Shu Yan away from him?!.
Chapter 896, "Are You a Male Model?", is the clearest early answer because it turns Chang Song's situation into a concrete plot event. The chapter gives readers a real answer by opening on Upon hearing this, Wen Jiaojiao seemed to think of something and...
Look to Chapter 13 for the clearest answer. It begins with Sensing that something was off with Jiang Yan, Jiang Yan dismissed the..., keeps building through What on earth do you mean?" Ignoring him once again, Jiang Li shifted her..., and lands on How could this happen..." Lin Manru didn't want to.
Chapter 659, "Bodyguard Agreement", is the clearest early answer because a shaky connection becomes usable in the plot. Early on, Besides, how easy is it to get into the Gu Family?. By the end, The woman who had defeated him and taken all his hopes..
Chapter 689, "Is the Soundproofing of This Private Room So Good?", is the clearest early answer because it turns Ji Yanbai's situation into a concrete plot event. A useful checkpoint is the way the scene starts with Jiang Li found the restaurant Shang Shaobai had mentioned, and had Ji...
Chapter 881, "How to Deal with Her Few Younger Brothers?", is the clearest early answer because it turns Zhao Lang's situation into a concrete plot event. The chapter gives readers a real answer by opening on After settling Jiang Li in the car, Zhao Lang fetched the medical kit...
Chapter 848, "Just an Adopted Daughter", is the clearest early answer because it turns Now's situation into a concrete plot event. Early on, With a "snap," the old lady slammed the photo onto the table, clearly.... By the end, If you need anything, Uncle Gu, feel free to let me know." Gu....
Chapter 725, "Illegitimate Children Can Also Inherit Property!", is the clearest early answer because it turns Jiang Cheng's situation into a concrete plot event. A useful checkpoint is the way the scene starts with Jiang Li seemed to have anticipated this answer and squinted, smiling...
Chapter 856, "Hurry and Stop Work!", is the clearest early answer because it turns Seeing Yu Li's situation into a concrete plot event.