Danielson or Pederson?

I've been trying to locate information about my grandfather, Harold, and his mother, Christine, over several decades.  Of course, the one solid source of information, my paternal grandmother Myrtle has since passed on.  But even when she was living, she didn't speak much about her husband Harold's history, or of his mother.   So I started my own investigation over the years, and have even more questions now.

Harold was born in 1900.  The most expedient way to track him as been through the Census records.   Working backwards, in
1940 he's married, living in Rural Marshall Co, MN.
1930 he's single, lodger with Theo Bergman, MN
1920 he's single, laborer to Ole Bergman (Theo's father)
1910 he's listed as nephew to Pete Hendrickson (so my assumption is he's Christine's brother)

Nothing else was found under Harold Danielson, however in checking the 1905 Minnesota State Census, I find Christine listed, age 33, and under her name I find Harold Pederson, age 4.  The age timeline follows in line with Christine through the other years I found her in the census.  And if Harold was born in 1900, in 1905 he could easily be 4 when the census was taken, before his birthday had arrived.  The above photo, line 51 shows Christine, and line 52 shows Harold.  It also shows that they both have been a resident of the state for 1year 8months, and in their current residence for 6 months.

Which leaves me with a number of questions, of course.  Most of all, why is his name listed differently?  A census taker error?   Where did they live the other 1year 2 months in MN?  and based on the way she is listed as servant, is she working for the Henry Nystrom family?

I searched Harold Pederson, there is one born the same year as my Harold in the same location to a Simon Pederson.

It's been told down through the family that Harold arrived in New York with Christine in 1903.  Again, time wise, this would fit with census information that in 1905 they'd been in MN for 1 year, 8 months.  However, I have not been able to find either of their names on any incoming ship manifest.  Were they using different names before arriving?  Did she come to this part of MN because her brother was already there?

So many questions, no solid answers.
Sometimes I think my grandmother was right:  "let sleeping dogs lie"
She never wanted to share or reveal whatever it was she knew.