Who decides after whom a theorem or conjecture is named? 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.
 A: The consensus 'decides'.
A paper gets published by a mathematician A, and is possibly read by other mathematicians. Someone who quotes the paper might refer to a certain statement in the original paper as 'the result proven by mathematician A'. 
If the result shows to be important in a certain field of mathematics, then the people in this field might start to refer to it as 'mathematician A's lemma/theorem', or something along these lines. If the result becomes more well known, maybe even proves to be relevant for mathematics outside the original field, then it might become colloquial to call it 'mathematician A's theorem'.
But it's also possible that the mathematician who first published the theorem named it after a concept he used in his earlier work, and people quoting it adopt this usage, etc.
There is no international council which assigns names to theorems, or even decides which result 'deserves' the label theorem.
A: 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.

