I can help you with the Gordlinia. We can and do list the intergeneric hybrids ("x" genera) after they are discovered and the research has been published.
Actually, some of these names don't last long because the ease with which two genera can be crossed is later explained by the lack of differences between the genera. XDigiplexis is one example. It was supposed to be a cross of Digitalis with Isoplexis, but all of the Isoplexis species turned out to be synonymous with Digitalis species. As a result, the plants were found to be Digitalis x Digitalis hybrids and no longer needed a special intergeneric name.
Inter-species crosses within genera are not included in our database, however, unless they occur naturally. They are included if they have cultivar names. One reason is that it would be a waste of time and resources to list every possible cross between the species of every genus. Another is that the names chosen for these crosses often are merchandising conveniences and have no basis in science.
Rosa x rehderiana is not listed on HelpMeFind.com, a database of more than 40,000 roses. It is not included in the major taxonomic databases, and GRIN even calls it an invalid name.
Your information about the rose, however, would be searchable if you were to write an article for ATP about this rose or create a thread in the Rose Forum to give us your information about this rose.