The surname dictionaries are singularly unhelpful when it comes to the origin of Bice, Bilkey and Boase, all found in Cornwall in the early 1500s and all three dispersing by the 1600s. Bice and Bilkey do not appear in Reaney’s dictionary of surnames while Boase is implicitly regarded as a variant of Boyse or Boyce. The Oxford Names Companion regards Boase as a first name, taken from the Hebrew.
Does their early geography in Cornwall offer us any more clues?
The surname Bice, usually spelt Bysse, is the most mysterious. By the late 1500s it was focused on the parish of St Enoder in mid Cornwall, which supplied most of the examples in the parish registers, on which the following maps are based. However, there was an earlier example of Bysse to the west at Crowan.
Bilkey appears to have had two early centres, moving out from those. One was immediately north of the Camel estuary while the other was to the north of Camelford. Were these two lines originally connected? The name is possibly a diminutive for someone who made billhooks. It has nothing to do with the abbreviated first name Bill, which came later.
Finally, we have Boase. The presence of the spellings Boyse and Boys in the 1520s at Redruth, Breage and on the Lizard and their overlap with the spelling Bose might suggest a shared origin with Boyce. This name was already widespread in the 1500s and even more so by the 1600s. It looks to have had multiple points of origin in west Cornwall.
Maps of all three surnames in 1861 can be found here.