The real Captain Avery was the leader of the Far Harbor's villagers and spoke against the Children of Atom. To calm the people down and prevent conflict, DiMA killed Captain Avery and altered a synth to look exactly like her and take her place in Far Harbor (even to the point where the synth would believe she is the real Captain Avery), but the duplicate would be open to the idea of the Children of Atom being on the island.
The following is based on unverified behind the scenes information and has not been confirmed by canon sources.
Her name is most likely inspired by the real life pirate captain Henry Avery, linked to the story of the likely fictitious pirate colony already referenced by Bethesda by way of the raiders stronghold Libertalia.
End of information based on unverified behind the scenes information.