I make the argument I mu book Medusa that the constellation of Perseus also represented Bellerophon (to the inhabitants of Corinth) and Hercules (to the inhabitants of Tiryns, while the constellation represented Perseus chiefly to the inhabitants of Argos. In each case the hero was the local hero of the city, and you can make an excellent case for identifying the surrounding constellations with elements of the hero’s myth (or, in the case of Hercules, one of his myths). just as Perseus rescued the princess Andromeda ( daughter of king Cepheus and Queen Cassiopeia) from the Sea Monster Cetus, so did Hercules rescue the princess Hesione (daughter of King Cepheus and an un-named queen) from the sea monster Cetus. In both cases a horse was involved, as well. That Perseus got identified with the constellation (which is just about as big as that of Orion, if not as impressive) rather than the more famous Hercules is a fluke of literature and astronomy.
On the other hand, there are stellar behaviors and details of the constellation that make it much more aligned with the myth of Orion. In fact, our oldest source, Homer, explicitly relates the myth of Orion to the constellation, and many of his acts and characteristics are uniquely associated with that constellation. Chief of these is his setting when Scorpio rises, representing his being fatally (or almost fatally, depending upon whose myth you buy) stung by the scorpion. There are a great many other characteristics that would take too long to go into now. I have discussed them in lectures that I have given, and intend to write a book about it, similar to my book Medusa.