Chances are he changed both his first and last names, and they could have been anything.
The only possible clue to his identity I find is his middle name:
The Washington censuses show his first children were born in Illinois, and the Illinois Marriage Index lists:
1 April 1876 Livingston County, Jeff Hansen Smith to Betthy Christine Overbeck.
They are in the 1880 Grundy County Illinois census.
In the later King County Washington censuses Jeff listed birth as April 1853 and immigration as 1873 or 1874.