With latest (currently 4.0 alpha 7) you can export a choice of strings by using PROPERTY_HINT_ENUM
:
ADD_PROPERTY(PropertyInfo(Variant::STRING, "character_name", godot::PROPERTY_HINT_ENUM, "Mary,Rebecca,Leah"), "set_character_name", "get_character_name");
Concerning the second part, I don't believe that modifying the choice list is currently possible with extensions - only with module development. The reason is that Object::_validate_property
is not available to extensions. See this discussion