Why is Proxima Centauri called Proxima Centauri? It seems very logical, to call the star, closest to earth, "Proxima" ("Proximus" is Latin for "close" and the word for star, "stella", is feminin, hence "Proxima"), but there's one thing I don't understand: in order to call a star ±"The closest one", you must be sure that in future, no closer star will be found.
This is not so simple: lots of very close stars, like Barnard's star, Kapteyn's, ..., are very weak and even not visible to the naked eye.
So, how can we be that sure that Proxima is indeed the nearest one? Have astronomers indeed examined the complete sky in order to prove this?
So, how can we be that sure that Proxima is indeed the nearest one? Have astronomers indeed examined the complete sky in order to prove this?


The minimum absolute magnitude for a star is, according to this well-known diagram about +16. Proxima Centuari is at the very low end of this scale with an absolute magnitude of +15.60. Still, it has an apparent magnitude of +11.13. That means that if a star is closer to us, it needs to be +11.5 or brighter. Every object of that magnitude or brighter has been categorized, and a hypothetical close star would've stood out due to its large parallax. So it's safe to say there are no closer stars ... at this moment.


  you must be sure that in future, no closer star will be found.


Stars move (they rotate around the galaxy center), so in the (far) future, there might be a star closer to use than Proxima Centauri, just like sometimes Venus is the planet closest to Earth, and sometimes Mars. So it's possible that Proxima might not be the nearest star in the far future. This is not something we have to worry in our lifetimes, though :)