I've been pondering this question because Shikamaru's name is from his dad's (Shikaku), Ino's name is from her dad's also (Inoichi); Shino is from Shibi and Choji is from Choza. Okay, maybe not all of the characters' names are from their dad's, but I'm just wondering. :D TIA
Naruto's father was Namikaze Minato, who had been Jiraiya's pupil.
As we know, Jiraiya wrote, and the main character of his first book was named Naruto.
Because he enjoyed the book so much, Minato chose to name his then-unborn son after the character of Naruto in the story, in the hopes that his son would too grow up to be just like the protagonist. Even though Naruto was not aware of this until sixteen years after his birth, he nevertheless is just like the protagonist.
From Naruto Wikia.
So Naruto got his name from a character Jiraiya created in one of his books.
In addition to the accepted answer, which is correct.. Jiraiya got the name 'Naruto' for that character while he was eating ramen. One of ramen's toppings is called 'narutomaki', and that's where Jiraiya got that character's name, 'Naruto'.
As you may know, Jiraiya was an author, as well as the teacher of Minato, Naruto's father.
His first book, The Tale of the Utterly Gutsy Shinobi featured a protagonist who held the ideals of Jiraiya and was called - Naruto (possibly named so after the food).
Minato liked the book very much and decided to name his son after this character.
I think Kishimoto gave naruto his name because it fit the theme of his mother's maiden village: the village hidden in whirlpools. Since Naruto roughly translates from Japanese to mean maelstrom or whirlpool, it is very likely Kishimoto bequeathed the protagonist name to be this since he already had his mother's last name, uzumaki, which means spirals or whirlpools.
Nagato was one of Jirayaya's students. Nagato inspired the hero of the story, and so the character was named Naruto, after him. Naruto's father then named his son after the character of the story.