Yes, I believe the article was originally called Double placenames, but was then renamed "List of ..." Somewhat confusingly, there is also a Wikipedia page, Category:Double-named places which refers to what would more accurately be called reduplicative placenames such as Pago-Pago. This suggests that "double" is rather an ambiguous term, since various sorts of doubleness are conceivable. Wouldn't "Amalgamated placenames" be more accurate?
As for Budapest, it's the notable example there of a completely merged spelling without any space. It would be good for this page to include a cities list of manageable length, let's say 10 items, but how could one define this: places with more than 100,000 inhabitants?