Guess it depends on how much you want to spend. You could cut some stitches on the rolled part behind the rivets, flatten the leather and put the tag there, for a cheap fix. But the more flat leather of a collar is on the dog, the more it wears, flattens, separates the hair on the neck. A small dog could mean half his collar is flat leather, while a large dog wouldn’t have that much because of larger neck size.
Does dog NEED a rolled collar because of hair issues? Or it rolled leather just a “look” you like seeing dog wear? You say dog doesn’t have much hair to prevent jingling anyway, so maybe just going with a flat leather collar for a flat name tag might be an easier alternative, than trying to make rolled leather work in this instance.
I have two hairy dogs, both wear rolled leather to prevent hair rubbing, tangling their long hair on the neck. They both have jingling tags because the County REQUIRES dogs outside to be wearing Rabies and License tags at all times. You can get a ticket EVEN in your own yard, if dogs are not wearing their tags. So my dogs have the ID tag, Rabies, License tags on and they jingle when dogs move around inside or outside. I don’t notice the jingle anymore, except if they should scratch a shoulder and spin the collar a bit. Does help me tell where dogs are hearing the jingle!
Way too many other things to get worked up over than a small jingle noise.