Yes, I do think "Titanus MUTO" is a name, because MUTO has become a name. The MUTO Superspecies Profile literally says that is their "Monarch designation," which is the exact same terminology used for the Titanus names. Logically if they have a designation, then they're not "unidentified," but that hasn't stopped Legendary. What we personally think about these things doesn't change how true or false they are in the canon.
Regarding MUTO Prime, at this point I think you are deliberately misunderstanding me. This entire time I've argued that "Titanus Jinshin-Mushi" is not a species. If it isn't a species, then the other MUTOs being related to her is entirely meaningless. The question is not whether they're the same species, it's whether that specific designation of "Titanus Jinshin-Mushi" should apply to the 2014 MUTOs, which it has literally never been used to. You can claim that "the back half of the Titanus designations is part of a taxonomic name" but I've already asked you for a source on that and you can't provide it. If you have nothing further to present, then I'm done responding to this.