Often, the surnames we have nowadays can differ from their ancestors of half a millennium ago. In the case of the three below the difference is subtle but nevertheless significant in identifying their origin.
There is a place called Trengrove in Menheniot, near Liskeard. But this was not the origin of the surname Trengrove. The Menheniot Trengrove was also spelt Trengof in the medieval period and is in fact an example of the common placename meaning smith’s farmstead. Like the placename the family name is a re-spelling of this more common name. The first example I’ve found is from the late 1590s in west Cornwall between Hayle and Camborne. Trengroves remained confined to this district until the 1800s when they headed eastwards (or maybe some Trengoves to the east independently began to add the <r> to their name.)
The surname Trenwith stems from a place in St Ives spelt Treyunwith in 1391 and Treunwith in 1508, meaning farmstead of the ash trees or possibly the farm of someone called Yunwith or similar. Sure enough, in 1524 we find a Thomas Treunwith at St Ives, one of the wealthiest men in that town. During the 1500s and 1600s the surname usually changed to Trenwith and some migration occurred to the east. This reached as far as Redruth (with a single example in east Cornwall at Calstock) by the 1700s. But it then contracted smartly back to West Penwith to huddle around Mount’s Bay in 1861, on the opposite side of the peninsula from its starting point.
Trescowthick only gained its <th> in the 1700s. Before then it was Trescowick or similar. It originated in the place also spelt Trescowick in the 1500s but now Trescowthick in Newlyn East south of Newquay. There a David Tresuyacke was living in 1543. The surname never strayed far from that part of mid-Cornwall until the eighteenth century, when branches sprouted both to the east and to the west.