I have never seen Sundgvist as a last name. It is written Sundqvist or (in the old days) Sundkvist. When someone emigrates, it might be written as Sundquist, but I've never seen that name with a g.
Fred is not a female Swedish name. It is short for Fredrika/Fredrica.
100023.26.41300,[Jämtland]_scb Jämtlands,.939, Births,Marriages,Deaths, 1888-1888, 0-0,Image 220 of 423
Apparently the priest got the father to confess since he is now listed as the father. However, note that the child is still listed (by a tally mark) as oäkta (illegitimate). This is an extraction of the full birth record I saw. The priest had a few months to "work on" getting this information after the birth. This particular extracted record was sent to Stockholm for statistical purposes after the end of the year.
You are lucky. Usually, if the priest finds who the father was, the father is listed on the original birth record. This time was different and the original record doesn't say but the extraction does.