On my current horse's halter I have his show name. On my old horse's halter it said his show name and then my name. The reason why I did not include my name on my new one's is because the plate was much smaller because the halter was smaller so it could only fit one name and I thought my horse's made more sense.
I always thought putting the horse's show name on the halter and your name or farm name on the lead rope was good. That was if you sell the horse, halter can go with it, but you can keep the lead and it'll still work for any horse!
I'd rather be riding!
If you don't plan on absolutely keeping this horse for a very long time, I'd suggest putting your name on it. Or if you plan to sell/lease it to someone (or if YOU lease the horse) i'd put the show name and your name on the halter. that way, when you sell or send off on a lease, the halter goes with him.
Nikki's halter has her show name on it. The only lead shank I have that has a plate was already engraved - it was an award one - otherwise, I use the cotton ropes that have a chain at the end...but I would get a lead plate engraved with my name.
My last name (conveniently short) on a brass tag on leads and eye-rings of my generic but good leather halters. They can be removed if they go with a horse I sell, or have a plate attached if buy the horse what will wear it. In the meantime, nothing walks.
My horse's two nice leather halters have his show name on them. His old crappy leather halter had his barn name on it. My two halters that I bought recently (grooming halter and quality nylon halter for bathes) have my first initial and last name on them. They only have first initial because there is another girl with my same last name. I mainly got these done this way because I'm leasing/selling my horse soon and these halters won't go with him.
His lead rope has a dog tag with his barn name on it. I would put your farm name or your last name on one though.
I put the show name on the show halters and call name on the barn halters. I put one of those round brass thingies on my lead ropes with my initials on them. Lead ropes have a habit of walking off when the grooms put the horses in turnout. Since we all use green lead ropes, I can go up and down the aisle and get mine back.
I have always done show names on the halter. I keep halters of horses I've sold - I have a little lineup of them on the wall next to my desk with their pictures above them. It's a really nice keepsake...