From csowiki
The index to the 1800 Census for Litchfield County, Connecticut gives James and his sons names as STERLING. A persusal of the actual documents shows this is not true. A little transparent red arrow points at the 'i's

Isaac Stirling 20 Jun 1773 son of James and Hannah
Elisha Stirling in Salisbury Township probably g-grdson of Wm of Haverhill
Thomas Stirling 6 Dec 1767 son of James and Hannah
Thomas Stirling duplicate enumeration in Goshen
Ephraim Stirling in New Milford Township g-grdson of Wm of Haverhill
James Stirling of Cornwall ( husband of Hannah May
Note that even the great-grandsons of William of Haverhill, Ephraim of New Milford, CT and Elisha of Salisbury have their name spelled STIRLING.
Editors Note: This is a reprint from a CSO 2003 Library article. With the latest DNA evidence tying the St*rlings of Accomac, Cornwall and Lyme together I thought it might be instructive to revisit the data.