Interesting story, I've heard it before.
But please bear with me here, as I'm not the sharpest dagger in the drawer: what does a splintered paddle and laws to protect the defenseless have to do with how Pahoa got its name?
I did find a reference to "pahoa" (spelled "paoa") in the Pele and Hi’iaka Legend:
Ka-moho-alii turned his canoe
To rescue lad Kane from Nihoa.
Anon the craft lies off Nihoa’s coast;
They shout to the lad, to Kane-apua,
Come aboard, rest with us on the pola.
Ka-moho-alii turns now his prow,
He will steer for the fertile Niihau.
He sets out the wizard staff Pa(h)oa,
To test if Kauai’s to be their home;
But they found it not there.
Once more the captain sails on with the rod,
To try if Oahu’s the wished for land:
They thrust in the staff at Salt Lake Crater,
But that proved not the land of their promise.
No idea if Nathaniel Emerson is considered a legit source, but here's what he has to say:
“One Hawaiian says [paoa] should be pahoa. (Paulo Hokii.) The pa(h)oa mentioned in verse eight was a divining rod used to determine the suitability of any spot for Pele’s excavations. The land must be proof against the entrance of seawater. It also served as a spade in excavating for a volcanic crater…When a suitable place was finally discovered on Hawaii, the Paoa staff was planted in Panaewa and became a living tree, multiplying itself until it was a forest.”
This doesn't explain how Pahoa got its name, but I'm happy to agree that the gods named it and leave it at that, because it's definitely my kind of heaven.
Thanks everyone for posting, and sorry for burdening you all with my confusion.