Apparently, you now can. TrueCaller is a mobile phone app available for all major platforms which enables the user to identify unknown phone numbers. It identifies the Caller ID by performing a search against a database that it maintains cataloguing phone numbers across the world. The company behind this software is True Software Scandinavia AB which is based in Stockholm, Sweden.
While the database was presumably initially populated with information available commercially or via reverse lookup services, the app (which is free) offers an option allowing users to let it transmit the phone's contact list to the company's server. As a result, unlisted phone numbers with associated contact information have been leaked unintentionally and stored in a database. The database can subsequently be queried by name. True Software has dubbed the end result a crowdsourced addressbook.
ET reports that TrueCaller is very popular in India:
The app's database, essentially, is a giant, collective, phone book. The mobile numbers of nearly every Indian Cabinet minister, heads of intelligence agencies such as the Intelligence Bureau and Department of Revenue Intelligence, and CEOs of India's largest companies are all on the database.
According to Alan Mamedi, COO and co-founder of app-maker True Software Scandinavia AB, the app has 1.6 million Indian users. India is the app's single largest market, accounting for nearly half of its user base. Assuming an average of 100 contacts per phone book and allowing for duplicates, the company now owns a database of 50-80 million Indian phone numbers.
While the company offers to delete entries from the database upon request, it's very likely too late when this is done - horse, bolted, stable door, etc. Things will be so much better if contact whitelisting became the norm everywhere.