I'm fairly sure nominatim does support official_name, see searching for lastminute.com London Eye...
In my opinion OSM should mirror Wikipedia in keeping the common names of stadiums instead of renaming articles or OSM objects when they get a new sponsorship names

Leyton Orient is your club? Have you checked out my 3D mapping of the stadium in F4map? https://demo.f4map.com/#lat=51.5600475&lon=-0.0123069&zoom=18&camera.theta=57.655&camera.phi=-118.619