Yeah, this is kind of the central tension with Civ switching.
In VI, you are absolutely not leading the same Egypt at the end of the game that you were leading at the start. You have new tech, new buildings, new wonders, new religion possibly, new civics, new units, new government etc. But yes, you are still called “Egypt,” and you still receive the same bonuses from flooded tiles and sphinx tile improvements, etc.
In VI, the evolving national identity is baked subtly into the game. In VII, it’s an abrupt cultural revolution after each Age.