Hierarchical namespace service with distributed name resolution caching and synchronization

A service enables a command that refers to a file system object using a hierarchical namespace identifier to be executed against the file system object in a flat namespace. The service selectively distributes the command to one of a plurality of name resolution nodes based on a directory name included in the hierarchical namespace identifier. The identified node resolves the directory name to a flat namespace identifier that is used to execute the command against the flat namespace. After communicating with at least one storage node to resolve a directory name, each name resolution node stores a mapping of the directory name to the corresponding flat namespace identifier in a cache, so that subsequent resolutions of that directory name may be performed more efficiently. Cache entries may be invalidated when an operation occurs that impacts the relevant mapping and/or based on system considerations such as cache expiry.