Monitoring the domain name space makes as much sense as monitoring trademark registrations. A monitoring service provides you with a chance to react as quick as possible to the mis-use of your names.
managed IP monitors domains registrations on a regional level (e.g. worldwide, per continent or TLD) and provides you with reports that include the domain names matching your names.
Single domain names may be monitored as well (e.g. to see if registered domains become available again).