The Barnum Family, 1350-1907 calls her Hannah Hurd (while providing no source for that name) and also calls her the mother of only four of Thomas' children. Other available sources give her surname as unknown and state that she was the mother of all ten of the children of Thomas.
Some well-documented research by Ann Tappero indicates that her given name probably was Hannah, but that Hurd almost certainly was not her surname. [see: http://freepages.genealogy.rootsweb.com/~tapperofamily/barnum2.htm#hannah for details]. Reference is made there to a Hannah Hurd born in Boston in 1640, the same year that Hannah Unknown was born in Norwalk, Connecticut. Those two persons are not related and had different husbands and children.
It is believed that the use of the name Hannah Hurd may have resulted from confusion with the name of the second wife of Thomas Barnum, Sarah Thompson, who was the widow of John Hurd.
A family group record in the LDS Church archives, submitted in about 1942, mistakenly shows the source for Hannah Hurd as The Families of Old Fairfield by Donald Lines Jacobus. When that source is viewed, using the page number given, reference is found to Thomas Barnum and his second wife, Sarah Thompson, but the name of his first wife is not mentioned.
Although at least one source says she was the mother of all ten children of Thomas he had at least two daughters with his second wife, born after Hannah´s death.