Toxteth had Vills belonging to Bernwolf and Stenulf in 1066, Smithdown had a Vill owned by Aethelmund, Woolton (Wibaldeslei) was under Lord Wulfbert, West Derby itself had various holdings for, amongst others, Gilbert, Warin, Theobald and the exotically named William son of Nigel, all under the Overlordship of King Edward.
Kirkdale and Bootle had their own listings. West Derby showed twelve demesnes, or holdings includes ploughlands, forest, Woodland, fisheries, and a church. It is interesting to speculate which might have been in the area that was to become Liverpool city centre itself. Given the topography, I’d put some money on the unnamed listing containing two ‘fisheries’ maybe being here, as the sea lake of the pool would be the easiest place to farm the fast flowing Mersey for its bountiful haul of fish and eels. The lack of a name for this place in the Domesday book could simply be that no-one physically lived there, or that the census-takers couldn’t be bothered walking down the steep hill when they could see that there was nothing of note there, or that someone had slipped them a groat or two not to notice, and thus avoid the inevitable taxation. Pure speculation of course as we can never know