Interesting. That far back, a "proper" surname is unlikely - they were just starting to go with "so-and-so of such-and-such", using place of residence as a descriptor.
I cannot confirm that Woodchurch, as such, existed at the time of the Domesday Book, for it is not listed. It is shown on the modern-day map, but without a Domesday marker, and the adjacent lands were held either of the Archbishop of Canterbury or Hugh de Montfort. The extant church dates from the 13th century, and further deponent sayeth not.
One Ansketil of Rots is cited with a number of holdings in Kent, but none particularly close to Woodchurch. He is thought by some to be the same as "Ansketil the archdeacon", who held lands in and around Deal, Kent. If so, he was a senior cleric and not that likely to have heirs of his own - possibly brothers and/or nephews, who would be hard to identify.
Yeah, no.
Sir Anketillus de Woodchurch Clarke/Clerke, I, {Fictitious}
Will clean this up when I get home today.