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As Gliese 436, and Gliese 581 etc these all are present in different constellations, also they are both at different distances from the Earth and both are discovered by different sources, but why all the are named 'Gliese'.

Is the anything common between these stars or what?

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They are found in the Gliese Catalog of Nearby Stars.

This kind of naming is nothing new, you may have seen NGC objects (listed by their entry in the New General Catalog).

There are a lot of catalogs.

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    $\begingroup$ In addition, because all the nearby bright stars have had names since antiquity, the Gliese star catalogue is mainly of dim stars - red and brown dwarfs. $\endgroup$ – Ingolifs Aug 9 '18 at 21:07
  • $\begingroup$ slightly related information astronomy.stackexchange.com/a/27279/7982 $\endgroup$ – uhoh Aug 10 '18 at 5:48

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