First thing I always do is do a google check on the name given and the email address, I think everyone does this already so no secrets, but a good first step.
google the name, email address, phone number in different variations and an ip address search here DNSstuff can let ya know location of person making the offer so if you have a guess on possible end users you can see if the location is a match, this is assuming you are running your own site or using a parking company that provides this information, if running anonymously with no information then it's all about knowing what your domains are worth to a business and sticking to your guns, if you make an offer on a domain I feel strongly about whether you say your real name or say Bozo The Clown my price will be the same as I'm not looking to sell the strong ones to anyone other then the perfect end user so playing games with anonymous people at lower offers doesn't interest me, if your domain could be legally challenged another reason to not engage in anonymous discussions until you know who you are dealing with, a lot of my end user sales they came right out and told me who they were and what they did which probably got them a better price instead of a higher price as I would rather see domains I profit from developed eventually and most of the end users I have dealt with so far seemed like decent people.