Barnoldby le Beck, in the Haverstoe Wapentake of Lincolnshire, is a difficult name. The first element is likely from the Old Norse male personal name Bjǫrnúlfr, rather than the cognate Old English male personal name Beornwulf, especially taking into consideration the heavy Scandinavian influence in Lincolnshire. The second element is Old Norse by ‘a farmstead, a village’.
The earliest reference to the Beck, from Old Norse bekkr ‘a stream, a beck’, is Barnoldby upon Becke 1662 Terrier.