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Having thought about it, I realise that naming compounds of two and four elements, be they actual pieces or game-specific aspects to a piece, but not all three is not that uncommon. Take the -elicopter pieces of Man and Beast 07: When Beasts Collide. There are compounds of every two dimple components of the Helicopter - Gnu, Anu, Hovercraft, Hajj, Cohajj, and Cohovercraft - the Delicopter - Nintu, Uluru, Dovercraft, Dajj &c. - and the Selicopter - Zebu, Zulu, Sovercraft, Sajj &c. - but none of three such components. The only exception that I can think of is the Buffalo, which is the only compound of three of the Gallop's four components. Were I to add prefixes for Pawns with three kinds of double-step move, it might be argued that I could add names fr Knight+Camel+Antelope and the like.
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One idea that occurred to me was to concentrate on the warhead and helmsman combinations and their components so that I could view the three-way combinations as trident++ambush, trident++nonchalant, European+helmsman, and warhead+helmsman. These might be termed triamb, trinon, eurhel, and warhel for short. It did however then occur to me that eurofighter would be illogical as it stresses the European component of the trident component and it would be more consistent to term it trihel. This would also have the advantage that eurofighter as an actual weapon has been renamed typhoon, which is also the name of an existing Chess variant. It would then be logical for patient, penitent, impenitent, and impatient to be renamed euramb, eurnon, waramb, and warnon. I would be interested to know what other people think.