Anna was baptized with the surname
Lund. I haven't checked her siblings.
In 1771, the inhabitants in the Duchy of Schleswig were ordered to give their children fixed surnames (much earlier
than in the Kingdom of Denmark). Many parents in Northern Schleswig
(Sønderjylland) chose to give their children
the byname by which the family was known in the local community (instead of a surname ending in
-sen). The fixed surname could come from either the paternal, or the maternal side.
You can read about this here (in Danish):
http://nfi.ku.dk/publikationer/webpublikationer/ddsoefternavnetshistorie.pdf/ - page 5
You see Anna's surname in the confirmation record 1806, but in the 1803 census she's recorded with her patronymic
Nissen. It probably took a while to get used to the fixed surnames.
Best regards,
Inger