Well I seem to have a few ideas:
Maybe...
"The butcher" -
Sphageus (ΣΦΑΓΕΥΣ)
"The horseman" -
Ippeus (ΙΠΠΕΥΣ)
"The Elder, The younger" (not to original but it could fitt) -
Ho Geraioteros, Ho Neoteros (Ο ΓΗΡΑΙΟΤΕΡΟΣ, Ο ΝΕΟΤΕΡΟΣ)
"The warrior" - maybe ideal for Spartans

-
Polemistes (ΠΟΛΕΜΙΣΤΗΣ)
"The poet" -
Poietes (ΠΟΙΗΤΗΣ)
"The philosopher" -
Philosophos (ΦΙΛΟΣΟΦΟΣ)
"The builder" -
Dometor or Ktistes (ΔΟΜΗΤΩΡ, ΚΤΙΣΤΗΣ)
"The slayer of barbarians" (maybe

) -
Barbaroktonos (ΒΑΡΒΑΡΟΚΤΟΝΟΣ)
Not all are truly positive but there have to be names for other Hellenistic rulers or not so great Kings..
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