The reasons for both omissions are debated in a sheaf of studies.
Actually they are less of a problem than it seems. Even when Moses is not named, his presence is felt.
Even when God is not mentioned, He is there at every moment. He even seems to like it that way, since He says, “Even if they forget Me, let them keep My Torah”.
People who had good parents and good teachers do not necessarily evoke their names all the time but know that their example and guidance are an unseen influence on all they do.
In my own career, I am on record as saying that I did not object if God were not mentioned in the preamble of the Australian constitution so long as the moral quality of Australian society showed the influence of God-given principles.