the myth is explained in the book. the only difference between 'philosopher's stone' and 'sorcerer's stone' is that the former provides a connection to a real myth.
At the time she was an unknown author with a single kids book. I think changing the title to make the theme more obvious was justifiable. Changing the term throughout the book was unnecessary.
Personally, I grew up with the Philosopher's Stone and always wondered why she chose that name. It was only years later when I learned it was a legend outside the books did it make sense. The book does explain the meaning in the context of the novel, but not the wider cultural significance. That dampens the impact (just like how the Crystal Skull is not nearly as impactful as the Holy Grail in Indiana Jones).