This spec has come up a couple times; the first time I wondered whether a simpler approach might be acceptable: * setting properties to be updated * omitting properties to be unchanged * explicitly setting 'undefined' properties to be deleted I've used that approach and github seems to have done something similar. I like the idea of a patch spec for JSON - it's required by a strict implementation of REST with HTTP PA…
This proposal is more in line with the system you describe (except null instead of undefined). https://tools.ietf.org/html/rfc7386 I prefer it, and think it's much easier to understand.
If you start with original.json, then client 1 applies add-middle-name.json, and then moments later client 2 applies change-name.json not knowing that the other patch had been applied, you'll end up with a possibly unintentional merging of the two. I'm assuming change-name here wanted to clobber the whole name object, and did not intend to merge and keep the middle name.
There's a couple ways around this. One is to code defensively and always pass the middle:null when clobbering the name, since you know other clients could set a middle name. The other is to do some sort of versioning check to ensure no one else has changed the document since you last fetched it. That could be implemented outside the json patch, using if-not-modified headers or something, though it is tempting to do it with the "test" actions provided in the main spec discussed here.