
I don't think it matters whose name goes first BUT it tends to be done so that the person whose address the dog is registered at have their name first. That's how it is for the dogs I co-own. Hence anything official will be posted to that address as well of course. Hence I have one dog where my name is second, he does not live at my address and the other owner's address is used, and I have another where my name is first as she does live with me and my address is used.
Remember you will have to set up an extra account with dog.biz etc to be able to enter shows online in joint names, also need a separate account with the KC if you want to be able to register pups and similar, as with everything it is one account per ownership.
There is no official set time for joint ownership, you can transfer back and forth to your heart's content -which many do. For instance I got a pup that was meant to be jointly owned, but we agreed I could add my kennel name to her name, so I transferred her from breeder's name to mine, added my kennel name, then transferred to joint names. Then the breeder and I decided we weren't going to breed from her for various reasons and my daughter got ownership of her, so we transferred her to my daughter's sole ownership. All that within a year. Next pup I got that was to be jointly owned I decided not to bother with my kennel name simply to save all the transfers!