Millennia ago, when only a few thousand stars, a handful of planets and nebulae, and some transient objects like supernovae and comets, were known, people usually named these objects after gods and heros, but also after everyday objects. Stellar constellations that vaguely resembled something known, was named after this. Mars is red, so it was named after the god of war; Mercury, being the fastest to complete one cycle around the Sun, was named the god of messaging and traveling.
With the advent of telescopes, so many objects are now known that we had to come up with a more pragmatic convention, so usually an object is named according to its place in some catalogue, its type, and/or it coordianates on the sky. For instance, a quasar detected at the "J2000" coordinates ${mathrm{dec.},mathrm{RA}} = {22^circ, 22', 56'', -09^mathrm{h}, 46^mathrm{m}, 36^mathrm{s}}$ may be called J2222–0946. An x-ray source observed in the constellation Cygnus may be called Cyg X-1, while its binary counterpart is number 226,868 in the Henry Draper Extension Catalogue and is thus named "HDE 226868".
Oftentimes, an object appears in multiple catalogues, and will thus have multiple names. For instance, a Lyman $alpha$-emitting galaxy appears in a catalogue of Ly$alpha$ emitters, but due to its infrared properties, it will also appear in some catalogue over dusty galaxies (though Ly$alpha$ emitters tend to contain little dust).
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