"In mathematics, a conjecture is a conclusion or proposition based on incomplete information, for which no proof has been found." This is what conjecture is according to Wikipedia.

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    $\begingroup$ Perhaps because Poincare did not prove it. Perelman did but didn't really "claim" it (in part because the proof was sort of "on the shoulders of giants") so the name Perelman's Theorem never really came into prominence. That said this is what it was called for quite some time. As those that knew it as a conjecture leave the field, its name will probably change. $\endgroup$ – Ian Sep 6 '17 at 1:44

Long-standing famous conjectures tend to keep their names even after they have been proven. Thus one still often sees "Catalan's conjecture" rather than "Mihăilescu's theorem", or "Bieberbach's conjecture" rather than "de Brange's theorem", or most famous of all, "Fermat's last theorem" rather than "Wiles's theorem".

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    $\begingroup$ It actually sounds fun to make a big list for such results. Another famous example I know is Bertrand's postulate (or Chebyshev's theorem). It is also fun to see that Modularity theorem (formerly Taniyama-Shimura-Weil conjecture) was stripped off of its old name. $\endgroup$ – Sangchul Lee Sep 6 '17 at 1:57
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    $\begingroup$ See here for such a list. $\endgroup$ – Robert Israel Sep 6 '17 at 4:50

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