This is a fascinating question as it touched upon a very interesting Rambam in Hilchos Melachim (10:9). The Rambam couples together with the law that a gentile is not permitted to study Torah or keep shabbos, even if he kept it during the week (as a regular shabbos) he is culpable. Furthermore he is not allowed to make his own festival. Says the Rambam, a general rule: A Noahide is not permitted to create his own religion for himself, and to perform commandments from his own ideas. Either he should convert and become a full fledged Jew or he should remain with the 7 laws given to him, and he cannot add or subtract from them.
The question here is, if the Ben Noach were to "create a religion" from the 7 laws would that be problematic? Or because he is neither adding or subtracting from the 7 laws it is not "creating" a religion.
I believe that the simple reading of the Rambam indicates that because the Noahide is not "creating" a new religion, but is merely identifying with the 7 Laws it would be permitted to call it a religion.
It is important to point out that earlier in the Rambam (8:12) he rules that while a gentile who accepts the 7 laws will receive a share in the world to come, this is only if the gentile accepts it as a decree from G-d, and that these are the laws that were commanded by Him through Moshe, and that the children of Noach were commanded to keep these laws. However if the gentile keeps them because they are logical, then the Gentile is not classified as a Noahide and he does not get a reward for his deeds, or is classified as a righteous gentile nor considered among their wise men.