Had a falling out with a co-owner, agreement states that dog will be released to full ownership to one of us, upon certain terms, that is fine. One of us is wanting to change the dog's name, is the signature of the other owner required, or will AKC change it with one signature?

As long as the dog has not won points, once the co-ownership has been disolved, the new (single) owner can apply to the AKC for a name change.

And you can't change the name without the co-owner's permission if the name contains the co-owner's registered kennel name.

You need ALL listed breeders signatures to change a registered name.

Here is the rule straight from the AKC web site:

"The name of an AKC registered dog may be changed provided the dog was whelped in the United States. Further, in cases where the litter owner(s) first individually registered the dog, the litter owner(s) written consent shall be required. A dog name containing a Registered Kennel Name cannot be changed without the written consent of the owner(s) of that Registered Kennel Name. However, no change in name will be recorded by the American Kennel Club after the dog has produced or sired an AKC registered litter or has received an award at an AKC-licensed or member event. Any name change must comply with all AKC requirements."

An award is any ribbon - not just points.