duplicate names, help needed

Hello, you wizards of Norwegian ancestry [:)] I am working on a family from the Hedmark area. The 1865 Norway Census lists the family this way: http://www.rhd.uit.no/folketellinger/ftliste_e.aspx?ft=1865&knr=0301&kenr=2225a&bnr=2157&lnr=000 Jens Olsen, father, stone mason, 1821 Elline Henriksdatter, wife, 1828 Hedevig Jensdatter, daughter, factory worker, 1848 Ole Jensen, son, 1853 Ludvig Jensen, son, 1856 Agnete Jensdatter, daughter, 1859 Josephine Jensdatter, daughter, 1862 Emilie Jensdatter, daughter, 1865 (also 2 boarders: Mathea Berntsen and Hanna Gronberg) The family emigrated to Utah, USA in bits and pieces as Mormon converts. Ole died and I can find a Norwegian marriage record for Ludvig so he did not leave Norway, as far as I can tell. I can find US records for Jens, Elline, Hedevig, Agnete and Josephine. Handwritten family records do not list Emilie born 1865. However, there is a child named Oveda Jens Seva or Emma Ovedel listed in these handwritten records. In them, she is born in Ephraim, Sanpete County, Utah, USA in 1869, with a note that she died about 1882. Those dates work with the rough idea of when I believe they were in Utah. My question is in several parts, but I wonder about the name. It seems unusual compared to other names in this family. And I also wonder if it was common to 're-use' a name of a deceased child in Norwegian families. In my husband's Dutch family this was done all the time. Can anyone offer any insight? Thanks so much.