Helium was named after the place it was first found, decades before anyone held a sample. That place was the Sun.
On 18 August 1868, during a total solar eclipse seen from India, the French astronomer Pierre Janssen pointed a spectroscope at the Sun. He saw a bright yellow line. In England, Norman Lockyer saw the same kind of line on 20 October 1868, without an eclipse. It sat close to the familiar yellow lines of sodium but did not match them, and Lockyer labeled it D3.
Lockyer concluded the line came from an unknown element. With the chemist Edward Frankland he proposed the name helium, from the Greek hēlios, "the sun." The Science Museum describes it as named after Helios, the Greek sun god. Sources differ slightly on the date: Etymonline gives 1868, while the Elementymology reference says Lockyer named it in 1869.
The ending is the odd part. Elements ending in -ium are usually metals, like sodium and potassium. Lockyer's element was assumed to be a metal, so it got the metallic suffix. The historian Mary Elvira Weeks called the name a misnomer for exactly this reason, since helium is a gas.
For years the solar element had no earthly proof. The Science Museum notes there was "much doubt (and even mockery)" over the discovery. Other claimed solar elements of the period, like coronium, turned out to be ordinary ones. Frankland himself later publicly renounced his part in the work.
Vindication came in 1895. William Ramsay heated cleveite, a radioactive mineral from Norway, and collected the gas it released. Its spectrum showed the yellow line. Per Teodor Cleve and Nils Langlet found it in cleveite independently at about the same time. Ramsay sent a sample to Lockyer.
By then the gas had carried a sun name for 27 years. The same Greek hēlios still shines in astronomy, in words for a sun-turning plant and for the closest point of an orbit.