How do I add additional labels/tags to geo objects already present in OSM?

When I search for New York County I want to get the manhattan data but it pulls up the data for new york city itself. I feel that simple things like this would be wonderful for cross compatibility. My company uses both OSM and google for various things and sometimes names can mismatch.

Another example is that to get the baltimore city county data in osm you have to search "baltimore" by county, whereas to get the baltimore county data you have to search "baltimore county" by county. It should let me search "baltimore" for baltimore county and "baltimore city" for baltimore city county.

So I'd love to get some direction as to how to get proper tags/labels added to those so they come up in search, and in case I found some more cases in the future, thank you! I'll keep looking but I'm very new here and it isn't obvious to me, sorry if there are already a thread asking this.

Specifically I'm using the https://nominatim.openstreetmap.org/ api to get kml for counties, zipcodes, cities, etc (and btw how do we add more zipcodes in there? they don't really seem to have geospatial data for those)