I use DomainTools to monitor the domain registrations of many companies, including my own. I do this for research for DomainInvesting.com articles, and I also use the information I can glean to learn what domain names are moving at large companies.
One important reason I think people should monitor their own company name and/or email address is to ensure domain names aren’t being registered under their business name without their knowledge. It would be fairly easy for someone to register a domain name, say a trademark name, under the name of someone else with a different email address. Obviously, nobody wants to deal with a UDRP proceeding or litigation for a domain name they don’t own or even know anything about, so monitoring is something I do automatically.
I use the daily registrant alert email from DomainTools to try and monitor domain names registered in my company’s name. Other service providers like Whoisology and DomainIQ provide similar services. For people worried about costs, using Google might even be helpful to a certain degree (do a company name search + Whois to get a very rough idea).
If a domain name is spotted with the Whois information in your business or personal details, a report for invalid Whois details can be filed at ICANN. This will alert ICANN and the corresponding domain registrar that the invalid Whois information needs to be checked/confirmed. People may also be able to get some extra help from the domain registrar if needed.
Without using various tools it wouldn’t be possible to know if a domain name is registered under your name without your knowledge. There may not be much that can be done to preemptively stop this, but at least there is at least one way to combat it.