GG-Gf first name - lots of variations! Help!

Hi, I'm having trouble getting past my great great grandfather, mainly because I can't seem to be able to nail down his exact name. No one in the family still living has it either, so that's no help. I see all these variations in official records (which I have a good number of): Barduns Anderson (land record for his farm) Badenus (1860 Iowa census) Bardieus (1870 census) Berdinas (1875 Minnesota census) Bartinus (1880 census) Berdinas (1885 Minnesota census) Bardinas (1895 Minnesota census) Bardenes (1900 census) Berdinus (1905 Minnesota census) So yeah, this doesn't help matters much. Is there a commonly used name that might be similar, or might one of these be correct? FWIW, the first born daughter's name is different on the four censuses I have, the first one at 1 year old is Betsy, the next is Bardina (11), then Bertina (15), and back to Betsy again (21). Before anyone ask if I have the right censuses, I can very that it's the same family by the neighbors consistently showing up at each and every census, and the kids might change names (like avove), but the ages and where they were born are consistent.