I often have a hard time understanding (a) why people use the word 'trademark' as if it were a verb, and (b) what basis various people use to determine the non-existence of a trademark.
I have gotten the impression that there are people who believe that a US federal registration of a trademark is the beginning and end of the story. It certainly is not. One can certainly have a valid trademark right in the absence of registration, and one can certainly have a registration and no longer have a valid trademark.
Whether the name of an organization also functions as a trademark depends on whether it is (a) capable of functioning as a trademark, and (b) actually used AS a trademark. Trademark rights accrue through use of the term in commerce as a trademark - i.e. a device which is capable of, and in fact does, serve in the minds of relevant consumers as a distinctive indicator of the source or origin of the goods and services with which the mark is associated. Whether there is a federal registration for the mark has little to do with whether the organization may or may not have an enforcible trademark interest in the term.