The reporting on the first reading of the Bueng Kan law in parliament included some discussion on the naming of the new province. The draft law, as well as all earlier reporting, named the province simply as Bueng Kan (จังหวัดบึงกาฬ), after the name of the district which will become the capital district.
Bueng Kan is simply the name of a swamp near the small town, meaning "black swamp". Apparently, some consider such a profane name to be not auspicious enough for a province, so I have so far seen two other suggested names.
Mentioned within a news report on the first reading is the name จังหวัดนครบึงกาฬ (Nakhon Bueng Kan province), literally translated "Black Swamp city".
From an historical point of view more appropriate is the other suggested name Chaiburi (จังหวัดไชยบุรี), as that was the name of the district Bueng Kan until 1939 [Gazette]. This name goes back to the Mueang Chaiburi, and was changed as in 1914 the seat of administration was moved from Chaiburi to Bueng Kan [Gazette]. if I am not totally mistaken, the original capital an name-sake is now in Tha Uthen district of Nakhon Phanom province, thus the name Chaiburi for the new province would only be partially fitting as the historical origin would not be part of it.
Which of the names will finally be used will be known soon, as the new parliamentary session has just started, and both the constitutional amendments as well as this province are high on the priority list. I read one report today already which suggests that the province will be in effect in April, thus it must be finalized within the next week.