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.