Of all the stars in our galaxy, only 100 or so of the brightest stars have proper names. Rigel in Orion, Vega in Lyra, Altair in Aquila, all have names handed down from Greek, Roman, and Arab astronomers from antiquity.
In the early 1600’s, just before the invention of the telescope, the astronomer Johann Bayer developed a system to name hundreds more stars using Greek letters. He usually named the brightest star in a constellation alpha (α), the second brightest beta (β), the third brightest gamma (γ), and so on through to the last letter omega (ω). Bayer’s system is still in use today. And it did not supersede the ancient names of the stars, so Vega in Lyra is also named α Lyrae, and the star Mintaka in Orion is called δ (delta) Orionis.
Of course, with only 24 letters in the Greek alphabet, Bayer’s system ran out of names. So more systems were devised. The British astronomer John Flamsteed numbered the stars in each constellation from west to east. Flamsteed cataloged up to a hundred or more stars in some constellations, though stars in the Bayer catalog were not given numbers. The nearby star 61 Cygni is an example of a star in Flamsteed’s catalog.
As more stars were discovered and mapped, more catalogs were developed. The Bonner Durchmusterung (BD) catalog, the Henry Draper (HD) catalog), and the Smithsonian Astrophysical Observatory (SAO) catalog are all examples, and you will come across these designations in star atlases. Nearly all of the stars you see with a backyard telescope will be listed in at least one of these catalogs.