If electrons and photons, and possibly more particles, exhibit dual character, why don't physicists create a new classification for them? Why describe them as both waves and particles. Why not rather create a new classification, which accurately describes their behavior?
Quantum-mechanics predicts particle-like together with the wave-like behavior of quanta very well, there is no need for another theory.
Furthermore there can not be defined a new "class" of particles since there is no clear border between particles which show only classical "particle-behavior" (see for example double slit experiemnt with fullerenes)
And if you like a name for this particles: Call them quanta :-)
The fact is its not "electron proton and more particles" its basically all particles and the fact that they show properties of wave as well that is why for fundamental understanding we describe all of them as a dual of wave and particles
I think your problem seems to be with the words 'particles' and 'waves' and you want a new word. But the fact is more than words these describe certain properties which all of us are familiar of.