If Anna's name is exactly Per Hans Anna Persdotter - then it's a farm-name (gårdsnamn).
I'm sure you've noticed how few first names were in use, and consequently how few patronymics there were. Shout Anders Eriksson and probably at least 10% of the men would respond. So, in some places - like Dalarna (Kopparberg was the county, Dalarna the province) - they specified which farm you came from. Per Hans would thus be the farm; called so because they called their sons alternately Per and Hans - Per Hansson would be followed by a Hans Persson who'd be followed by a Per Hansson etc.
A woman marrying and moving to another farm would take the name of her new home. And so would a man! A man might marry an heiress and on moving to his wife's farm he'd take that name - this was called to take the chemise-name (ta särknamnet). However, if a man moved to his wife's farm, sometimes they would change the name of the farm.
Farm-names were really made illegal when proper surnames became mandatory (the Name law of 1963). This of course did not stop people using them, but you could not get the farm-name on an offical paper. However, the Name law was changed in 1982 and now allows for farm-names. We have e.g. a rather well-known singer who is called Busk Margit Jonsson - and Busk is the farm Margit comes from.
Ingela