I really have no problem with the term owner, but then words rarely bother me. Legally, I am her owner; she is my property. She's mine to keep and take care of, and nobody else can take her from me.
In the "how we live together" sense, there is no word to describe it. She's my child - I wipe her eye boogers away, and when her feet get cold in the snow, she runs to me with her paw in the air so I can warm it between my hands. She's my best friend - we love the same activities, and get so much joy from sharing them. And she's a lot more too. There is simply no good way to describe it.
In the "how we live together" sense, there is no word to describe it. She's my child - I wipe her eye boogers away, and when her feet get cold in the snow, she runs to me with her paw in the air so I can warm it between my hands. She's my best friend - we love the same activities, and get so much joy from sharing them. And she's a lot more too. There is simply no good way to describe it.