When you get a new horse please, please, please get the passport registered in your name. Officially you’ve got 30 days after buying a horse to get the passport registration changed to the new owner but if you’ve forgotten and have let it slip you can still do it past this date. Usually there’s either a form in the back of the passport for this purpose or you can download one from the website of the agency that issued the passport. It will need to be signed by the previous and the new owner so to avoid complication get it done when you pick your new horse up.
Not only is it a legal requirement but if the horse hasn’t been registered to you it also makes it very awkward if you come to sell the horse. You’d be surprised how many people don’t do this and it can become a real headache further down the line!