His Norwegian name was Tof Gregarsen Storli (Tof, son of Gregar, from Storli farm).
Vinje Chruch book 1856, baptism nr 17
http://www.arkivverket.no/URN:kb_read?idx_kildeid=1422&i...His father was Gregar Tofsen Storli. Rural Norwegians at that time had no family surname. As an individual surname they used their patronym and/or their farm name. Here in Vinje church book most witnesses to the baptism use their farm name as surname. So when Tof arrived US he might call himself Tof (Tov, Thov) Gregarsen or Tof Storli. Both would be correct.
The Americans expected people to have one established family surname, and they often made some ledgend to explain why the immigrants changed between their two surnames, the patronym and the farm name.
In 1865 census, the name was spelled Thov.
1865 census Storli farm:
http://digitalarkivet.no/cgi-win/WebCens.exe?slag=visbase&am...The father, Gregar Tovsen, died 19 Nov 1874
http://www.arkivverket.no/URN:kb_read?idx_kildeid=4822&i...