FamilySearch lists the surname of this family as"Bengson." Other sources cite their name as Banson, or Benson.
The obituary of James "Benson" states that he came to Utah in 1862 but he and his family appear on the 1861 Monarch of the Sea ship manifest as "Bengtsen" and both James and his wife Hannah were rebaptized on 3 November 1861 at Mill Creek, Utah under the surname "Banson.". The family was still in Mill Creek at the time of the 1870 federal census of Utah under the surname "Benson." James' Utah death certificate also reads "Benson" as do the Find A Grave memorials of both James and Hannah. Their son "Neils Benson" and their daughter Anna or Annie "Benson" were baptized as children at Mill Creek on 13 November 1864. James "Benson" paid tithing at Mill Creek in 1866.
Further research is needed to determine the name of the pioneer company with which the family crossed the plains.