you can get the monthly-generated iNaturalist Taxonomy DarwinCore Archive, which includes separate files for each set of common names: https://www.inaturalist.org/taxa/inaturalist-taxonomy.dwca.zip.
it doesn’t look like there are many names set up for Hindi, and even fewer that are set up with India as the place ID (which i think is the only way to get them to show up properly until Hindi is more fully translated).
to check on taxonomy between DarwinCore Archive exports, you could use the API to see taxa in bulk. for example, here are all the taxa within the genus Murraya. if a local Indian name exists, it will show up in the Common Name column: https://jumear.github.io/stirfry/iNatAPIv1_taxa.html?preferred_place_id=6681&taxon_id=123748&per_page=100