Thank you for responding and editing that so quickly.

If you think "Cultural Quarter" is used commonly enough you could add it as a "loc_name": https://wiki.openstreetmap.org/wiki/Names#Local_names_(loc_name)

Currently, a Nominatim search doesn't match anything for "Cultural Quarter, Oldham" https://www.openstreetmap.org/search?query=cultural+quarter%252C+oldham but adding it as a loc_name would fix that.