The Cambridge Grammar of The English Language p313-318 lists a number of verbs that allow alternative patterns of the form
verb + NP1 + PP(NP2) / verb + NP2 + PP(NP1)
A sample with the attendant discussion omitted,
i a. He presented a prize to Kim. b. He presented Kim with a
prize.
i TO or WITH credit entrust furnish issue present provide serve
supply trust
ii WITH only arm equip regale reward saddle
ii a. He blamed the accident on Kim. b.He blamed Kim for the
accident.
i a. She sprayed paint onto the wall. b.She sprayed the wall
with paint.
ii a. She loaded hay onto the cart. b.She loaded the cart with
hay.
i theme or loc brush cram hang inject pack plant shower smear spread
sprinkle
ii theme only immerse lean place push stand
iii loc only
cover decorate drench litter surround
i a. I engraved my initials on the ring. b.I engraved the ring with my
initials.
ii a. I scratched my initials on the ring. b.∗ I scratched the ring
with my initials.
iii a. ∗I labelled my initials on the ring. b.I labelled the ring with
my initials.
i theme or loc embroider inscribe mark stamp tattoo
ii theme only carve copy draw print write
iii loc only adorn brand decorate illustrate tag
i a. They hunted deer in the woods. b.They hunted the woods for deer.
ii a. ∗She searched her key in her bag. b.She searched her bag for her
key.
i quest or loc fish hunt mine poach stalk
ii loc only check dredge examine inspect investigate
ransack scour search survey watch
i a. He hit the stick against the fence. b.He hit the fence with the
stick.
ii a. He stabbed his knife into me. b. He stabbed me with his knife.
iii a. He pierced the pin through my hat. b.He pierced my hat with the
pin.
bang bash beat hammer jab knock
pound strike tap thump
i a. She built a shelter out of the stones. b.She built the stones
into a shelter.
ii a. They produce fuel from sugar. b. *They produce sugar into fuel.
iii a. ∗I changed a bedroom from the attic. b.I changed the attic into
a bedroom.
i goal/source assemble bake carve cut develop form grow make mould
sculpt
ii goal only compose construct derive design manufacture
iii source only alter change fold turn work
The idea is that these verbs allow alternate patterns of complementation with the same valency (2 complements), but with the semantic role of the direct object and oblique object switched. There doesn't seem to be a special word for this on a level with monotransitive, ditransitive, etc.