The name is a compound and an ordinary one: gichi, great, and manidoo, a power of the other-than-human kind. It is the name used at the opening of ceremonies, in prayer at the drum, in the naming of a child, and at the giving of tobacco, and for most Anishinaabe people today it is simply the name of the highest.
What is addressed under it is not described in the way a deity with a biography is described. Gichi-Manidoo has no stories of the kind Nanabozho has, no domain in the sense that a Greek god has one, no image and no cult centre. The relationship is conducted through offering rather than through narrative: tobacco is put down, words are said, and the transaction is with a presence rather than with a character. That absence of story is itself informative, and it is what makes the comparison with a European high god misleading in both directions.
Nor is the address exclusive. A person who prays to Gichi-Manidoo also deals with the manidoo met in a fast, with the thunderers, with the beings of a particular lake, and with the ancestors, and there is no sense in which the greater makes the lesser redundant. The system is not organised as a hierarchy with delegated authority.
Practice here has also been in long contact with Christianity, in some communities for three centuries, and many Anishinaabe people hold both. That is not syncretic confusion to be untangled by an outsider; it is the ordinary religious situation of the Great Lakes.