The conversation you all have been having today while I was at work has been instructive and entertaining, and I'm grateful for every contribution. Here are my responses, in no particular order.
I'm okay with putting Blekre in the "other last names" category in Anna's case (or in every case). I only made it the current last name because that was what the Norway Project suggested. I've read several g2g posts which hashed out the question of Norwegian naming; there were many different points of view, all with valid reasons, but I can't say I formed a strong opinion of my own.
The only area where I've diverged from using the patronym as LNAB is the male Blekre line, first of all because my family owned the Blekre farm for at least 200 years, but mostly because they brought that name over with them when they emigrated. It was my mother's maiden name, and it's so rare in the U.S. that any Blekre here is a pretty close cousin of mine.
I asked the question in the first place partly because Anna Olsdatter is such a common name. In fact, most, if not all, the unsourced trees I've seen elsewhere claim that Zakarias Jakobsen's mother was also Anna Olsdatter. I would like to attach Anna to her parents at some point, but I'd rather leave her an orphan than attach her to the wrong parents.
I may take too much for granted when I find trees on Ancestry that were created by Norwegians (especially when they match my DNA). Also, these people were farmers, not aristocrats. I can't imagine anyone wanting to graft their family onto my family's tree. So, in my zeal to connect my Norwegian lines to the larger tree, I may have been less than rigorous in my research.
Thanks again for all the information and constructive criticism. I appreciate it!