That's a more definitive answer than I ever dreamed possible. And, yes, I am a biologist too and know the basics of the nomenclature.Technically neither of the names you gave are correct, but I know what you're getting at. The first issue with the names you gave is that the genera are misspelt. They are actually spelt "Chamaeleo" and "Trioceros". Secondly, the first letter of the genus is always capitalized, but the species name is never capitalized. Thus, the two names you listed should be "Chamaeleo melleri" and "Trioceros melleri".
Getting to the root of your question, however, Trioceros melleri is the current scientific name for this species. As we learn more about the relationships between different species, occasionally species are transferred into different genera, or genera are split into multiple genera. In the case of T. melleri, the species was actually originally described as "Ensirostris melleri" in 1865, however in 1920 the species was transferred into the genus Chamaeleo as Chamaeleo melleri. In 1986, the genus Chamaeleo was split into two subgenera: Chamaeleo and Trioceros. At that point, the species was most accurately known as "Chamaeleo (Trioceros) melleri", however it technically was not incorrect to simply omit the subgenus, making "Chamaeleo melleri" equally correct. Finally, in 2009 the two subgenera of Chamaeleo were elevated to full genera, making the species now Trioceros melleri.
Hope that helps.