How to distribute credit in this situation? A mathematician Alice discovered a general idea that certain important mathematical object should exist. However she could not construct it rigorously on the technical level in full generality. Nevertheless she published two papers: in the first paper she rigorously constructed the object in a special case of independent importance; in the second paper she generalized it further to rather auxiliary situation which later became technically useful for the next case of maximal generality.

However to construct the necessary object in maximal (and natural) generality she was missing some background in another field. A mathematician Bob, an expert in that another field, has provided a missing argument upon her request. Together they wrote the third paper thus constructing the object in maximal generality.


  The question is how one should call the new object: Alice-Bob object or just Alice object?


Alice feels that the name Alice-Bob object distributes the credit equally, which is unfair in this case: the general idea belongs to Alice, and she could make it rigorous in some cases and published alone two papers on that. On the other hand, Bob feels that the name Alice object is also unfair as his contribution is not reflected. 

The new object started to be used in the field and people started to name the object in various ways without knowing the details I explained above.
As noted in the comments, it would be best if Alice and Bob didn't try to get either of their names on the object. That smacks of both egotism and insecurity, and is a recipe more designed to create bitterness than scientific progress.

Instead, this type of complexity is exactly what related work sections are for, in which you can say something like:


  Homogeoisopolymorpholisms were first identified in [1,2], then generalized in [3].


and let credit be distributed over time by citation and by ongoing work.  Alice and Bob, as current leaders in this subfield, are in a good position to set a descriptive name, and if they do so and insist that others use it rather than using people's names, then they are likely to have a strong influence on the name that does get adopted.

In contrast, fighting over which person's names are on the object seems likely to damage what appears to be a productive collaboration, and to prevent Alice and Bob from publishing a future set of high impact papers together.