I do this all the time, especially on international itineraries where on a single ticket I might credit various sectors to UA, TG and SQ. I always try to ensure that the BP shows the correct program name/FF#. On rare occasion, I might have to send in ticket stubs, but the mileage has always credited. Note, however, that you run the risk of double credits, where two programs occasionally are credited for the same sector. This has happened to me numerous times, and of course I always immediately call up and beg the FF program people to remove my unearned credits...