TITLE: Who decides after whom a theorem or conjecture is named?
QUESTION [13 upvotes]: Who decides after whom a theorem is named?
When someone discovers and proves a theorem, it is almost always named after that person. But how about when person A conjectures a theorem, and B proves it? 
Sometimes it is called the theorem of A (Fermat's little theorem, proven by Euler), sometimes the theorem of A-B (Ramanujan-Nagell equation), and sometimes the theorem of B. (Falting's theorem, conjectured by Mordell).
There are other cases where deciding the name would be more difficult - for example, when A (Ramanujan) and B (Ljunggren) conjecture it independently, and C (Nagell) proves it. (The example is the case of the Ramunjan-Nagell equation.) There is also the interesting case of the Stark-Heegner theorem.

REPLY [19 votes]: To complement the previous answer:
Arnold's Principle: 

If a notion bears a personal name, then this name is not the name of the discoverer.

Berry's Paradox:

Arnold's Principle is applicable to itself.