The genus name is the scientific name. You can check whether it is a valid name, and the names of described species in Index Fungorum. Type Termitomyces, search, and you'll find a list of species.

http://www.indexfungorum.org/Names/Names.asp

there are several monographs on the genus Termitomyces which is freely available on the internet. i think you have gathered the macroscopical data. now check its microscopical features, i think you could identify the species. if you can't access to those monographs send me your email, i would send you the monograph available to me on the genus.