Judy - wow, what a wealth of information to sort through there!! Definitely gives me some information to compare and start sifting through!!
The one you listed with the sibling, Sigrid, caught my eye, because Carl's first daughter, born in Philadelphia in 1912, was named Sigrid. Not proof or anything, but I wonder if she could have been named after his sister.
Question regarding the last name(s) - if I understand correctly from a very quick Google search about formation of Swedish surnames....
Karl's patrynomic last name would have been Svenson because his father was Sven. Bergman would have been the family name.
Sven's father would have been Olaus, then?
And they would have been alive during the time frame when family names were just beginning to be adopted on a regular basis, and patrynomic names fading out? So perhaps Carl dropped his patrynomic name and adopted his family name when he came to America?
Definitely a lot to think about!! Wow!!
ETA: Also, I am definitely seeking a death certificate for him too....just trying to pin down a year first, since I have to look through the death record index to get the record number, in order to request a copy.