The Andersen family came to Utah between 1863 and 1864. They likely came in 1863, the year Peter took out a PEF loan and they sailed to America. But the first documentation to place them in Utah is a church ordinance for Peter and Hanne in July 1865, which was prior to the arrival of that season's emigration. Further research is needed to narrow the year of their travel.
The inscription on his gravestone and his death certificate show his name as "Anderson."