How does the community decide whether to name a model/theorem after an author?
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.