Hallo David!
In that case that you are not so familiar with the swedish name-traditions, I can tell you that (with a few rare exeptions) there were no Andersson families in the early 19th century. Rather few people, in particular on the countryside, had family names. Instead they had patronymika: the father´s christian name followed by -son or -dotter (=daughter). The only thing you call tell from a name like Andersson, Persson or Månsson (in this early period, it changed within the period c1860-1900 to steady family-names), is that the bearers had fathers with the names Anders, Per (or Peter) and Måns (or Magnus). Probably your Johanna Andersson was an Andersdotter from the beginning, but were changed to Andersson. That is also a pattern, typical for the second half of the 19th century, parallel with the assuming of family names.
In the cities, family names were more common. But they were generally not of the type Andersson or Svensson, but of the type Hellström, Löfgren, or Borg (the same type of name as Flodstrand). Again it was not unusual with a combination of a patronyikon and a family name: f. ex. Lars Johansson Lundberg. Even in that case you can be sure that the father´s name was Johan (or Johannes, Jan, Jöns or other name with the same origin), but you can never be sure that the father was called Lundberg too. It could as well have been assumed by Lars himself.
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