Addresses with no street names

Most villages in Romania don't have street names at all, and typically people use "Main Street" in where it is absolutely required to put a street name. However, the official address, as is written in the national ID, contains no street name, just a house number. Many villages have houses spread out on a network of streets, not just along a single main street, so using "Main Street" in OSM doesn't seem like a good idea. Is this supported in any of the OpenStreetMap search applications (like Nominatim) or having a street name is a must? I would like to be able to search for "<house_number>, <village_name>, <country>".