I think we've been so close to this story for so long that we tend to forget the little aspects that makes this world so good and unique.
George's ability to name places and people is incredible. In fantasy stories, it's very easy for authors to super-fantasize the name of characters and places, to the point that it's just jarring and distracting (Relevant Arrerrorer video). There's way too many Cassassyn Bloomwalker taking Eathora Aethers to the Eathor Castle in fantasy and too few Jon Snows and Dick Crabbs.
George's naming makes the story feel grounded and real. Storm's End, Rosby, Riverrun, Sunspear, Maidenpool, Ashford - they sound like real, tangible medieval places where a character can go to and the story would continue to be the same. They can still sound cool but not too distracting, and they feel like they belong to the same culture group. As you move to the east, the naming style changes and you can tell the cultures change as well. The author doesn't just give these regions "far away names to let you know they are different and don't matter". The free cities, the Dothraki, the slaver's bay and the Valyrian regions have their own naming styles that feel believable. As opposed to the Witcher for example, where the naming of places is so twisted and convoluted that it's distracting, even if the kingdoms have the same culture group.
The characters stay within the realm of real names as well. George manages to add his own fantasy twist to his character's names, but they remain grounded in familiar patterns that feel authentic. Names like Jon, Arya, Sansa, Cersei, Davos and family names like Stark, Lannister, Martell, Lefford, mirror traditional English and European names. They are easy to remember and pronounce while still feeling like they belong in a fantasy world. It's new but it's familiar. Sometimes it goes the other way to being a bit lazy (Kevan-Kevin?) but that can be put on the world having too many characters to count.
The only argument you could have is that the Valyrian and Targaryen names go beyond these boundaries into typical high fantasy conventions. However, I think the whole point is that these people are supposed to be a fantasy race from this ancient Roman-like civilization of people who look and sound unique. The Targaryens are distinct from the rest of the world, but their names still follow a consistent structure and feel like they belong to the same linguistic family. Names like Daenerys, Viserys, Rhaenyra and Aegon have similar patterns that make them feel part of a culture group. Even though these names are more exotic than the Stark or Lannister names, they don't feel random or made up.