Question: Why is the Princess called Peach instead of Toadstool and why is the main villain called Bowser instead of King Koopa?
Answer: It's probably because the fact that the princess isn't actually from the Mushroom Kingdom. Mario tells her that she didn't look like she was from the Mushroom Kingdom, and she replied that she didn't know where she was from. She also said, "My earliest memory is arriving." This states that she probably came from a different world or came from Earth. Also, Bowser is a turtle, not a Koopa. Besides, he also has yellow Yoshi soldiers.
Answer: Maybe the Princess's name was already Peach, but she just hasn't said since she was a baby. And Bowser doesn't just have Koopas in his kingdom; he also had other things, like all the yellow guys called by the name of Yoshi.
Answer: "Princess Toadstool" was used in the original English-language manual, but she was Peach in the original Japanese, and that name continued in later versions, being combined with Toadstool. Bowser was originally called "Kuppa", but presumably the English-language version resonated more with people, plus removed any confusion of "Kuppa, King of the Koopas", so the English version stuck.