The entry in the RI Death Index identifies Benjamin's parents as Daniel & Alice.
In the 1850 Federal Census, Benjamin N. & Eliza Remington are living at Cranston, RI. They have two young daughters -- Sarah F. & Mary A.
In 1860 the family is still in Cranston. B. N. & Eliza have four children: Sarah F., Mary, George H., & Edward E. Next door is Francis Larose and family -- probably Eliza's brother. He is also born in Canada.
In 1870, 1875, & 1880 they are in Providence. In 1880 three of their children are with them: Mary A., Edward E., & Philip K.
His middle name as Nelson came from familysearch.org