[QUOTE=meghan1963;8554710]
have the papers in your name is true proof of ownership in cases if a dispute ever arises (it may seem like this might never happen to you but it really can - its crazy)
also in cases of loss for insured horses it is important[/QUOTE]
No and no! 
It does not matter whose name the registration papers are in. Equine Breed Registries have a policy of staying out of this type of dispute, as they simply provide registration papers on the horse, not proof of current title or ownership. As many people are familiar with, especially in the open performance world (i.e. hunter/jumper, dressage and eventing), a horse can change ownership 2 or 3 times with the registration papers never being transferred. It does not mean the last person recorded as owner on the registration papers is the current legal or rightful owner of the horse.
I have been retained for many court cases in which an ownership dispute has occurred. The ONLY true proof of ownership is a bill of sale, which is a legal document that transfers the title of the horse.
As a Certified Senior Equine Appraiser, I do many, many death claim reimbursements for insurance companies. The fact that an owner has not transferred their horse’s registration papers into their name does NOT affect the horse’s fair market value in any way. 
To the OP, whether you decide to transfer the papers into your name or not, please, please make sure if you ever resell the horse that you make sure his registration papers go with him. As well, if you have decided not to show him under his registered name, please be respectful of the breeder and make sure the breeder’s name, sire, dam and your horse’s registered name are included on his USEF number application so he can be found in the USEF database and the breeder and sire are able to earn points if your horse earns points any at USEF shows.