I'm pretty clear on the concept that in Hungary I should only get in a taxi that I have called for, but I'll be arriving from Vienna on the train (for the flight home I will have the hotel call) and wondering how to ensure that I'm getting into a cab that has indeed been dispatched for me. In other words, 10 other people might also have called XYZ cab company, and be waiting for their cab, how does everyone sort this out? Or is there a better option?
Lets start with the premise that you should not get into a cab that you did not call. The only real reason for this is that the fare will be unregulated and you will pay too much. How much too much? Maybe $20 for a $10 ride, This isn't unique to Budapest.
If you are having the hotel send you a car they may send you a recognized taxi company, but most often they will send a private cab, Either way it will cost you somewhat more; but not drastically so, Again not unique to Budapest but Hotels have "arrangements" with various companies or drivers, If this is a pickup arranged well in advance then my guess is that there will be man with a pieced of cardboard with you name on it, If you are calling the hotel when you arrive then you will be given a car number or told to look for the man with the cardboard,
Or you cab call the taxi yourself, I like CityTaxi but there are a number of good companies, +36 121 11111
When you get off your train if you are on one of the outside tracks go into the main arrival/departure hall. When facing the font wall of the train station look for doors on your left leading outside, Go through those doors and you will find the drop off / pick up loop,