The name "Toromiro" is related to an older term, inherited by Maori as "Miro", and in New Zealand referring to the same tree. It is of Proto Eastern Polynesian origin, that is, as far as we can tell, it was first used by the Polynesians who left Samoa for the Eastern Pacific, eventually colonizing Tahiti, the Marquesas, Easter Island, Hawaii and New Zealand and the other islands in this huge region.
In Tahiti it refers to the (northern) Polynesian miro (or milo), Thespesia populnea, with its beautifully-grained hard wood which was prized for building canoes and carving, and had a special status as a sacred tree, with its branches used in religious ceremonies. In traditional Tahitian religion, a priest holding a branch of the sacred toromiro could communicate directly with the gods.
In Rapanui (Easter Island), the word toromiro refers to what looks like quite a different tree, closely related and very similar in appearance to our large-leaved kowhai (Sophora tetraptera). However, this too was the tree which was prized by the people for qualities very much like those of the Thespesia, and its wood (now obtained from Chile, where Sophora toromiro also grows natively) is still used in Rapanui carving. Seeds from the last indigenous Toromiro tree still alive on Easter Island were salvaged by Thor Heyerdahl on the Kon Tiki expedition, and these seeds have enabled the slow process revegetation with this species to begin on the island.
There is more information and commentary on both the words miro and toromiro, and the plants associated with these names, in the entry for miro.