Until now, the quartet have been referred to simply by the number of protons in each atom - 113, 115, 117 and 118, respectively.
The elements are the first to be included in the famous table since 2011, and complete its seventh row.
The names must go out to consultation for five months, but if there are no objections their confirmation should be a formality.
This will come from the International Union of Pure and Applied Physics and the International Union of Pure and Applied Chemistry.
All four elements are extreme - the synthetic creations of scientists.
None of them exist in the natural state and were made by bombarding two smaller (albeit still very large) atomic nuclei together.
Theory predicts there are "islands of stability" where certain combinations should stick and hold together - but even then this state is usually only fleeting.
No element heavier than uranium, with 92 protons and 146 neutrons, has been seen for a prolonged period outside the laboratory.
Nonetheless, the exercise does provide scientists with valuable insights into the structure of atomic nuclei and the properties that stem from it.
As is customary, the discoverers of the new elements got the right to suggest a name.
The rules state that this can reflect a mythological concept, a mineral, a place or country, a property or a scientist.
The name also has to be unique and maintain "historical and chemical consistency". This explains why there are a lot of "-iums" in the table.
Nihonium references the Japanese name for Japan. The atom was discovered at the RIKEN Nishina Center for Accelerator Science.
Moscovium was named after the Moscow region, the location of the Joint Institute for Nuclear Research in Dubna.
Tennessine recognises the US state of Tennessee and the local contributions made to the discovery by the Oak Ridge National Laboratory and Vanderbilt University.
Oganesson honours the nuclear physicist Yuri Oganessian, who has played a leading role in the search for new elements including the one that will now bear his name.
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