If you search for almost any eponymous topic in Wikipedia, you'll find that it was first studied by someone else. For example, the Gaussian distribution (according to Wikipedia) was first studied by de MoirveMoivre. It seems that in many cases, naming the body of work was given to the person who first applied its study to some other field (using the earlier example, Gauss used the distribution in astronomy).
The common story goes that L'Hopital L'Hôpital bought "the rights" to L'Hopital's L'Hôpital's rule, as he was a nobleman and not a mathematician by trade, although I am not sure about the veracity of that story.
Although I am no expert on the history of Mathematics, it seems as though ideas or formulae assumed their names from certain mathematicians due either to a.) the more notable application or publication of the theory or b.) attribution by mathematicians of a later generation to pay tribute to (or garner attention from) the work of their predecessors.