In the New Kingdom, Anhur, a war god, gained the title Saviour, due to the feelings of the benefits of going to war to assert your own freedom, and so he became conflated with Horus, who shared both these characteristics, as the warrier against Set, with the title Saviour of his father.
The identification of Anhur as Horus, referred to as Horus-Anhur, was given a new name during the egyptian period of dominance over Nubia, when the kushites named him as Arensnuphis (also Arsnuphis, Harensnuphis), Ari-hes-nefer in Egyptian, meaning something along the lines of Horus of the beautiful house.
In a certain few areas, Horus was identified as the son of Banebdjed, who was an obscure version of Osiris, technically his Ba, worshipped in Mendes, and consequently also the son of Hatmehit, the local chief goddess of Mendes who had become considered Osiris' wife.
The aspects of war, and saviour, shared with Horus, contributed to Anhur's eventual identification with the much greater Horus.
During the egyptian period of dominance over Nubia, the kushites named Horus-Anhur as Arensnuphis (also Arsnuphis, Harensnuphis), Ari-hes-nefer in Egyptian, meaning something along the lines of Horus of the beautiful house.
Consequently once Osiris became identified as an aspect of Horus (and vice-versa), Arensnuphis was viewed as having Isis as his wife.