Pluto was the notorious god of the Underworld. His name derives from ploutos, 'wealth', with Liddell and Scott explaining, 'because corn, the wealth of early times, was sent from beneath the earth as his gift'.
However, there are other 'gifts' to be found below the ground apart from corn, and Pluto's wealth must surely have also included the precious metals that even in classical times were mined from below the earth. A more modern school of mythologists suggests that the god's name, like that of the Eumenides, was a euphemistic one for Hades, and that it was borrowed from Plutus.
The planet Pluto was discovered and named quite recently. The American astronomer Percival Lowell, who died in 1916, deduced that it must exist, and it was actually first discovered by another American astronomer, Clyde Tombaugh, in 1930. Several names were suggested for the newly found planet, with Pluto finally chosen by 11-year-old Venetia Burney of Oxford, England.
It is a most suitable name, since Pluto was the brother of Poseidon (Neptune) and Zeus (Jupiter), and these two planets were already present in the line of planets that now numbered nine. Further more, Pluto is a fitting name for the planet that is the farthest from the sun and so in an 'eternal night' like that of the Underworld.
Finally, there is a nice tribute in the name to the astronomer who calculated its existence, since the first two letters of Pluto are also the initials of Percival Lowell! One wonders if the little girl who proposed the name was aware of all these happy parallels and coincidences.
The Romans borrowed the name from the Greeks both in its untranslated form and also as Dives ('riches') which was contracted to Dis (see this name). (There was also in fact a Titaness named Pluto who became the mother of Tantalus. Her name has the propitious 'riches' sense as well.)