The first thing I usually do is run a Google search for the person’s name. This usually doesn’t give me enough identifying information since the majority of inquiries either only have a first name or have a common enough name that I can’t identify the person with certainty. I then try to search Google for the email address. This works better and can lead to a plethora of information, including domain registrations, website and/or forum posts, and other pieces of information that can prove to be useful.
I also use several tools (some require paid accounts) to identify domain name registration information. I use DomainIQ, DomainTools, and Whoisology to see what other domain names the person owns. Although this doesn’t always yield information about why the person is inquiring about one of my domain names, it can show me whether the person is a domain investor or operates businesses online and owns domain names.
I like to look at similar domain names to see if the person inquiring owns them. I usually start with the .net, .org, .CO, and some other derivations of the domain name where applicable. This can be helpful when there is something, but most of the time there isn’t anything related.
