It depends on when you ask.
Early in Egyptian history, Isis was firmly associated with the heavens—with the star Sirius in particular, and even with the sun—but She was not considered a Moon Goddess.
Moon Gods were the norm for Egypt—Iah, Thoth, Khonsu, and Osiris are among the most prominent and the moon’s phases were quite important to the ancient Egyptians. Scholars generally agree that the first Egyptian calendars, like those of so many ancient people, were lunar based. The temples marked the moon’s changes and celebrated the waxing and full phases, though they are somewhat silent about the waning moon. (If anyone knows of a good scholarly source for information on the Egyptian lunar festivals, please, please tell me…I am still searching!) But the face the Egyptians saw in the moon was masculine rather than feminine.
The Greeks and the Romans, on the other hand, were all about the Moon Goddess. In fact, the moon itself was simply called “the Goddess.” People spoke of doing something “when the Goddess rises.” They would kiss their hands, extending them toward the rising moon, “to greet the Goddess.” Magical texts give instructions for performing a certain working “on the first of the Goddess,” meaning at the new moon.
Because so much of our information about Isis came from these Moon Goddess-loving people, today when we think of Isis, the moon is one of the first things we associate with Her. Yet, interestingly, it seems to have been a third century BCE Egyptian priest named Manetho who first connected Isis with the moon. By the following century, when Plutarch recorded the most complete version of the Isis-Osiris myth we have, the tradition of Isis as a Goddess of the Moon was firmly established—even in Egypt.
Of course, it was easy to associate the fertility-bringing moon with the fertile Mother Isis. The ancient world also associated love affairs with the moon (the romance of moonlight, you know) and, in Her passion for Osiris, Isis was a famous lover. Of course, the moon and the obscuring darkness of night were connected with magic, too—and Isis was one of Egypt’s Mightiest Magicians from the beginning. One Egyptian story told how a particular magical scroll—which the tale calls a “mystery of the Goddess Isis”—was discovered when a moonbeam fell upon its hiding place, enabling a lector priest in Isis’ temple to find it.
Today, we also connect the moon with emotions, the deep, the waters, the feminine (taking our cue from the ancient Greeks and Romans, no doubt), the home, Mystery, and change (to name but a few). And Isis can definitely be associated with all of these things—from the emotional passion of Her myths to Her ancient Mysteries and Her enduring role as the Goddess of Regeneration and Transformation.
So is Isis a Moon Goddess? She certainly has been for millennia. Whether we choose to honor Her in this form has more to do with us than with Her. A modern NeoPagan will probably be quite comfortable working with Isis as a Lunar Goddess; a Kemetic Reconstructionist, less so. But Isis is a Great Goddess; She is All, and so She is unquestionably to be found in the deep and holy Mysteries of the Moon.
For myself, while I do find Her in the moon, I resonate more strongly with Isis of the Stars and Isis of the Eternities of Space. Nevertheless, I feel called to explore this aspect of Her. And someday, when a beam of moonlight illuminates my own inspiration, I fully intend to create a series of lunar rituals with Isis as their heart and soul.