Marvel's the family that became the Fantastic Four.
The origin of the Fantastic Four is classic and is firmly rooted in the 1960s. In Fantastic Four #1, Reed Richards, his fiancée Susan Storm, her brother Johnny Storm and friend Ben Grimm raced to launch on a rocket to study the effects of cosmic rays "...unless we want the Commies to beat us to it!" (according to Sue Storm). The rocket crashed after reaching the storm, and the four were irreparably changed - especially Ben Grimm, who unlike the other three was completely unable to shut off his powers.
Reed quickly realized the four could use their new abilities to help mankind, and thus became the Fantastic Four, giving himself the name Mr. Fantastic in the process. In Fantastic Four #489 written by Mark Waid with art by Mike Wieringo, Reed Richards tells a bedtime story to his daughter Valeria and recounts the day the four were transformed. "Once upon a time," he begins, "there was a very arrogant man who did something very stupid." Reed talks about his guilt regarding the fate of his friends, and realized he had to change how the world saw them. "'Mr. Fantastic.' Does that sound like something anyone would really want to call themselves? No."
Reed Richards chose the name as part of a grand strategy: he wanted to provide his friends with the life of celebrated heroes, complete with heroic costumes and adoring Fantastic Four fans. As he puts it, "...glamour and fame weren't options. They were necessities." Reed wanted to give Sue, Johnny and Ben exciting lives and all the opportunities in the world - all so they would forgive him for his disastrous decision that made the team in the first place.
Thus, the attention-catching name "Mr. Fantastic" was deliberately designed as a part of Reed's goal to paint his family as heroes, not beings to be feared. What appears to be a self-serving name is actually one chosen out of guilt and shame - two feelings Reed feels even to this day (considering that the Thing still cannot be cured and is trapped in his orange rocky form). Reed Richards may have named himself "Mr. Fantastic," but he certainly doesn't see himself that way.