I believe that Carin, as suggested by the geni.com profile at https://www.geni.com/people/Anna-Persdotter/6000000022049275452, is probably a good reading.
The first letter has an extra curlicue at the top, but the second is an old-fashioned "a", the third looks like the "r" in "Perßon", and the last two letters are clearly "in", with the dot of the "i" shifted a bit to be over the "r" because of the loop from the "h" in "hustru" above.