The story
Partly uncertain. Oldest Domesday Book attestation is Tuxfarne. The first element is likely the Old English personal name *Tuk (modern day Tuck/Tucker), genitive singular *Tukes. The second element is now ford, but this is clearly a reinterpretation from the second earliest attested form Tuxforne (with vowel mutation), which leaves the original -farne element still unexplained. The modern form is equivalent to Tuck's ford.
Etymology from Wiktionary, CC BY-SA 4.0.