Is there a name for the unusual transitive status of the verb "to pile"?

This is the Spray/Load Alternation
(Verb class 9.7 in Levin 1993, English Verb Classes and Alternations pp 117-119).

Some examples of the phenomenon, from the link (which also has a list of verbs that take it). Ungrammatical sentences or phrases are marked with initial asterisk, and references are to other alternations in Levin 93.

• Jessica sprayed paint on the table.
• Jessica sprayed (*on) the table with paint. (Spray/Load Alternation: 2.3.1)
• Paint sprayed on the wall. (Causative Alternation: 1.1.2.1)
• *The wall sprayed with paint
• Jessica squirted/splashed/sprayed water at me. (Conative Alternation: 1.3)
• a spray of paint (Zero-related Nominal)
• *a spray of the wall
• Jessica loaded boxes on the wagon.
• Jessica loaded (*on) the wagon with boxes.
• *Boxes loaded on the wagon
• *The wagon loaded with boxes
• *Jessica loaded/stuffed/crammed boxes at the truck
• a load of boxes
• *a load of the truck

Compare the Spray/Load verbs with the Fill verbs, also on the link.

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.