Why is Princess Toadstool now called Princess Peach?
For gamers who were first introduced to the Mario series in the NES and Super NES eras, the princess that Mario has to rescue on a regular basis was known as Princess Toadstool. That's what the instruction manuals and the in-game text say - so that's her name.
When I was a young kid, I thought the princess had a pretty funny name. From my interpretation, toads are a type of frog, and stool can literally mean crap. So um, I thought she was being called the princess of frog crap. Maybe there's a meaning to Mario's frog suit in Super Mario Bros. 3 after all, maybe...
I didn't realize until I was 20 years old that "toadstool" can mean mushrooms (should've looked in a dictionary), so Princess Toadstool being the princess of mushrooms, that makes a whole lot of sense, given the series regularly takes place in the Mushroom Kingdom.
In Japan, the princess was always known as Princess Peach (Pichi-hime). For some reason when Super Mario Bros. was released in 1985, Nintendo decided to go by Princess Toadstool for the English name instead. Unlike American peaches which tend to be more red, orange and yellow on the outside, Japanese peaches are actually pink, which is quite suitable for Peach since she loves to wear pink!
Real Japanese peaches - source: Jpninfo.com
When Super Mario 64 came out in 1996, the Princess's letter to Mario was signed "Princess Toadstool, Peach" - it served as a way of unifying the names in both regions. There were still several Princess Toadstool references within Super Mario 64, but going forward in all future Mario games, she was only known as Princess Peach.
Anyone that has played Mario games in the last 20 years will be familiar with the name Princess Peach. Even if you liked the original name more, after seeing it long enough, it'll stick. Not to mention it's much simpler to just call her Peach.
I'd expect kids to be more shocked when they see "Princess Toadstool" when they play retro games like Super Mario Bros. or Super Mario World and start Googling the question.
If you find the name Peach unusual, then most likely you are probably someone that is old, and haven't played a Mario game for a long time!
As for the reason why Nintendo changed the English name to Princess Peach? Unfortunately none was ever given, beyond making the name consistent between both the Japanese and English editions.