How does the community decide whether to name a model/theorem after an author? In this question I asked:

Assume that Jane Doe has published a paper in 2010 where she has developed a model or a theorem or a similar result, let's say for concreteness that it relates to &quot;growth&quot;
Now assume that Jane Doe is writing another paper in 2015, where she refers to the model/theorem from her paper in 2010.
Is it acceptable for Jane to write: &quot;Doe's growth model (2010), implies that ...&quot; or &quot;Doe's growth theorem (2010) implies that ...&quot;, or even &quot;The Doe growth model (2010) implies ...&quot;?

The answer seems to generally be &quot;no&quot;.
@jakebeal states:

&quot;Newton's Laws&quot; and &quot;Hawking radiation&quot; and &quot;Rayleigh scattering&quot; are retrospective judgements of significance by the community.

@user2768 states:

Writing &quot;Doe's growth model&quot; or &quot;Doe's growth theorem&quot; suggests that the community has agreed to name Doe's results this way.

This leaves me with the question: How does the community come to agree to call such a model &quot;Doe's growth model&quot;? By what process is this decided?
There is no concrete way that I know of to determine the name of a model or theorem. In the past the following methods seem to have applied: 


The author calls it something to refer to it and then it gets famous and everyone else uses that name. 
The author doesn't name it but just talks about the subject and the idea through multiple papers. The papers become famous, and people start referring to it as "The Auther's Blank."
The author comes up with an idea based on previous work, and in crediting the inspirational work, ends up calling it "Original Author's Special Idea" which then is how other people refer to it until said name becomes common. 


While I personally believe that naming it after yourself is bordering extreme hubris a bit too much for my own comfort, I imagine that it's tough to refer to some nameless idea. My suggestion would be to give the specific model a name that doesn't use your name. This will emphasize the fact that it needs a name and that you're not some narcissist trying to name everything after yourself. Then, if the model proves useful, others also have a convenient name for it -- preferably something close to what you referred to it as in the original paper.

For example, if I were writing that, my reference to the model would be something like: "In the 2010 paper _______, Doe [and the other authors attributed fairly] put forth the model ____, termed  for brevity." Then I would describe the model and how it relates to the work.