Jobs said in an old video that one reason he called the company Apple is that he likes apples a lot.
Jobs said that one of the reasons the company was named Apple was that it would be Ahead of Atari in the Phone book.
Jobs said that the deadline he set for choosing a name came and so they decided to settle on Apple computers.
Jobs said that as they re-examined the name, they found that it matches Apple's core value of simplicity and that's one reason the name was kept.
In the book Steve Jobs by Walter Isaacson, it was mentioned that Jobs said that he was just on his way back from the apple farm and that's one reason he decided to call the company Apple.
According to Walter Isaacson, Jobs found the name Apple to be fun-spirited and not intimidating and this was one reason he liked it.
In an old video, Steve Wozniak who is Apple's co-founder, said that when Steve Jobs suggested the name Apple they couldn't come up with a better name so they decided to stick with it.
When a PR agency told both Jobs and Woz that the name Apple must be changed because it doesn't symbolize the power of computers, they replied saying that it symbolizes the fact that computers are coming to homes and that Apple's were a good home symbol.
Because Steve Jobs was on a fruitarian diet, he was thinking about fruits a lot. This fact made the name come to his mind faster.
While there is no evidence that this factor affected the choice of the name, the first Apple logo had Newton sitting below a tree with an apple fruit hanging above him. This made some people conclude that the name Apple referred to Newton's apple.