Sallah: Please, what does it always mean, this... this "Junior"? Professor Henry Jones: That's his name. (points to himself) Henry Jones (points to Indy) Junior. Indiana Jones: I like "Indiana". Professor Henry Jones: We named the dog Indiana.
When a character needs a name that tells the audience right away how awesome they are, this trope is one way to do it. The character will have a first name that's interesting and long - at least three syllables long - contrasted by short and unremarkable last name.
Similarly to Mister Strangenoun, the first name is sometimes a cool-sounding noun that isn't normally used as a name. It could also be a made-up word, or an actual name, but only one that's rare enough to still sound unique.
For the last name, "Smith" and "Jones" are the two most used, but any one-syllable name that sounds common and unremarkable also works.
TimeSplitters has an entire family of these spread across all three games and several centuries. The three that are introduced are Peekaboo Jones in 1965, his great-great-grandfather, Elijah Jones from the 1800's and Mordecai Jones from the Robot Wars in the 2200's.
Sci-fi author Robert A. Heinlein was very fond of this trope, most often with the surname "Smith". His characters included Valentine Michael Smith, Woodrow Wilson Smith, and Johann Sebastian Bach Smith.
Arabella Figg, Nymphadora Tonks (and Andromeda Tonks, nee Black), Broderick Bode, Caractacus Burke, Bartemius Crouch, Elphias Doge, Marvolo Gaunt, Augustus Pye, Pomona Sprout, Emeric Switch, Emmeline Vance, Romilda Vane, and pretty much all the other Blacks. Thank you, Wikipedia.
In L. Sprague de Camp's Solomon's Stone, the hero finds himself in a world populated by the figures people daydream of being. Everyone has a Sesquipedalian Smith name, indicating first the daydream and then the mundane reality.
The Zork games feature a character named Antharia Jack. He's a movie star known for playing Indiana Jones-style roles, but his character's name is his own.
Capability Brown (not his real name)... and his Discworld counterpart: Bloody Stupid Johnson (his less famous contemporaries being Sagacity Smith and Intuition de vere Slade-Gore.
Former US President Rutherford Hayes
Preceded by Ulysses S. Grant.
Some Naming Guides actually suggest giving longer names to children born in families with a small surname.
Harrison Ford. Seems like the Indy connections have come full circle.