Olivey is claimed to have come from the Latin saint Oliva, although it’s just as possible it was a variant of the name Oliver, from an old French first name. Oliver was quite common in sixteenth century Cornwall but I can find no Oliveys that early. The spelling Olivey first appeared on the Lizard and in West Penwith, at St Keverne and Sancreed respectively, and at roughly the same time – in 1605 and 1607. By the mid-1600s this name had multiplied but was confined almost entirely to the two districts of the Lizard and West Penwith.
Oxenham is clearly an English placename and probably came originally from mid-Devon, near Okehampton, where the surname was also found. Oxenhams had arrived in the far south-east of Cornwall – at Antony and Landulph – as early as 1544. From there, or perhaps directly from Devon, the family name, usually shortened to Oxnam, spread surprisingly widely. It was particularly prevalent at St Columb Major from the 1570s while also found in the 1600s still at Landulph but also at a scatter of places in east Cornwall and at Gerrans on the Roseland. The dispersal continued into the 1700s when Oxmans (this spelling first appearing in the 1620s), Oxnams and Oxenhams were found from Paul in the far west to St Wenn, just west of Bodmin.
The exact origin of the name Palamountain is less certain. Richard Polmonter at Newlyn East in 1543 suggests an origin in the place Pollamounter in the same parish. This was spelt Polmounter in 1576. However, the baptism of Cateren Polmanter at Sancreed many miles to the west in 1577 may indicate a second origin in the Polmanter at St Ives. The meaning of these two placenames is unclear. Craig Weatherhill suggests that Polmanter at St Ives (originally Porthmanter) may mean ‘gateway to stone-land’ (from men and tyr). Moreover, it’s quite possible they may not possess the same elements – the pol at Newlyn East could well be pol (pool).
While there were no other examples in West Penwith after 1577, the surname, usually spelt Pollamounter, flourished at St Columb Minor and nearby parishes from the 1570s. The spelling Pollamonten first appeared in the Breage parish register in west Cornwall in 1641. It established itself there during the 1700s while Pollamounter remained the spelling in mid-Cornwall. It looks likely that Palamountain was a specific spelling variant emerging at Breage, although whether the Palamountains were originally Pollamounters from the east or Polmanters from West Penwith remains open to question. Family history is required to prove a link.