Ma'at Thoth and Anubis have aspects of one god , Ra - Jehovah, Allah or Waaqaa. In Ma'at you can get the character or nature of Thoth or Anubis. Or in Thoth. . . Or in Anubis. . . In other words in Ma'at is Thoth, in Thoth Anubis etc.
You can't say ancient Egyptians were Polytheists
Ancient Egypt was solidly polytheistic, as were all ancient Near Eastern civilizations prior to Judaism. The modern deities Jehovah and Allah emerged from cultures which were originally polytheistic. It is a complicated and much-discussed topic, but not a mystery. The ancient Egyptians, Nubians, Libyans, Canaanites, Mesopotamians, Persians, Anatolians, Greeks, and Romans all encompassed a myriad of male and female deities within their religious beliefs.
I can't speak authoritatively on Waaq, who was worshipped in Somalia and Ethiopia and other points to the south and east of pharaonic Egypt. Waaq does not belong to the ancient Near Eastern tradition, so my knowledge on this god is limited. I can say with confidence that except for Punt, the ancient Egyptians themselves rarely ventured this far to the southeast, and if they did happen to come across people who worshipped a god named Waaq, they do not seem to have commented on it in any of their own records.
One must take care in connecting the concept of the Christian Trinity with ancient Egyptian deities. While the Egyptians did see certain deities as family groupings—Amun, Mut, and Khonsu, as one example—this did not tend to happen till later in dynastic times and the pairings were quite distinct in nature and function from the Christian Trinity. The Trinity represents three forms of God in one, while to the ancient Egyptians these divine family pairings represented different and distinct deities. Using my own example again, Amun and Mut and Khonsu certainly were not thought to be three forms of the same god.
Your topic is not the first time, Abba mudda, that I've come across the idea of Egyptian deities all representing the same god. It is in fact an old theory, but no longer a functioning one in proper historical research. It grew out of very early studies of ancient Egypt when most scholars had received traditional classical educations and Christian upbringings, and it was a direct result of Christian bias. Even Re, with his plethora of manifestations, did not represent the many within the one. All of the many examples of synchronism attributable to Re happened largely in later periods, but for complicated socio-political reasons and not for any intention of monotheism.
When one studies the ancient Egyptian religion on its own terms, it is perfectly clear that the ancient mind saw this as what we today call polytheism. There were many gods. Over the course of pharaonic history, in fact, the Egyptians accrued around 2,000 different deities. Some more or less died out in the early periods (e.g., Andjeti), others arose later (Osiris and Isis), some were brought in by foreigners who had migrated into Egypt (Kadesh), and many were not even named. They appear anonymously on tomb and temple walls in texts such as the Book of Gates.
Anubis was definitely a jackal god, Abba mudda. That is clear. The Egyptians happened to love dogs and kept them as pets, and we see them depicted on occasion on stelae and other monuments commissioned by their masters. The artistic stylization is distinct: Anubis was fashioned in the religion from a species of North African jackal (which is itself part of the dog family, of course). Anubis is one of the oldest deities in the pharaonic pantheon but is only one of numerous jackal deities—Khentyimentu, Wepwawet, and Duamutef being other examples.
As far as I am aware Anubis has no connection with Sirius. Its epithet "Dog Star" is not even part of the Egyptian tradition. Other Egyptian deities were eventually represented by this star, but not Anubis. In fact, as ancient as he is, Anubis and his purpose changed little in 3,000-plus years. He was a benevolent underworld deity and guardian of the cemetery.
Thoth and Anubis do have certain connections, but generally only in an underworld sense. While Thoth does have lunar connotations, this role was not his most important. He was principally the deity of writing, wisdom, and magic. He is most often depicted with an ibis head, and usually only when depicted as a baboon is there a lunar connotation. But as for Thoth and Anubis, we see them together in later funerary texts like the Book of the Dead and together on certain items of burial equipment such as sarcophagi—but even then they appear distinct from each other and possess different roles.
Maat is not directly connected with either of these dieties in any traditional divine familial role, although Thoth was often depicted as "revealing Maat." Yet in this sense it was not so much the goddess herself as it was the concept represented by her name: cosmic order and balance.
None of this is related to Christianity. Egyptian deities belonged to a religious tradition that far predated monotheism, aside from the brief attempt of the king we call Akhenaten who was responsible for the so-called Amarna interlude, but that's altogether different. It's been my experience that many laypeople go too far in connecting Judaic and Christian traditions with ancient Egypt. While some degree of influence was certainly there, it's much exaggerated in modern circles. Christianity began as nothing more than a minor sect of Judaism, and Judaism itself grew out of the pagan Canaanite culture and was much more influenced itself by Canaanite religious practices as well as by the Zoroastrians and Greeks.