Very good point

I would create a new glossary for each doctor:
Doctor-A
Doctor-B

Then I would include your main glossary into each of these glossaries and, of course, I would include the DoctorA-Names glossary to Doctor A and the DoctorB-Names glossary to Doctor B. So when the Doctor_A glossary is highlighted you get all your entries of your main glossary plus the names as desired by Doctor A. Same for doctor B.

Now when you add a new entry and you use the default Add Hotkey ALT= the entry will be added to the highlighted glossary (either Doctor-A or Doctor-B). That is fine for specific entries that only are used by Doctor A (or B). However most of the new entries should rather go to your included Main glossary which is the "common" glossary for these doctors. To achieve this just create a new Add hotkey entry where you specify the target glossary:
{AddGlossaryEntryDialog}
filename = "Glossary\Main.xglo"
input = "text"
moveToTop = "n"
resumeUponOK = "n"
{/AddGlossaryEntryDialog}

When using the hotkey you assign to this entry, it will open the Add window of your main glossary.