Go to the RHS registration site. Jose Marti was registered in 1959. It is a cross of Bob Betts x Bow Bells. If you search this cross, you will see that both Jose Marti and Mother's Favourite come up. MF, registered in 1990, is listed as a "synonym", meaning it was not the originally registered cross. Technically, MF should never have been registered. The RHS has the category of synonym for entries just to deal with these duplicate registration issues. I suppose you could call the plant Jose Marti Mother's Favourite to recognize both registrants but MF is not a varietal/clonal name of JM. My bias would be to call plants by the original registration name, in this case JM.
We have a similar situation with some clones of plants having been awarded under two different clonal names, even though both plants were the same clone. For example, Paph Maudiae 'Bankhaus' was later awarded again as 'The Queen', when it shouldn't have been awarded again. It is very hard to keep track of crosses and clones so it is no surprise that duplicates happen.