That one's straight up called the Elvis Operator.

I hate it when things like this get names that everyone's supposed to know and it's considered a mark against you if you've never heard it before, but I do think the name Elvis Operator is hilarious. :D

Also, a lot of other languages (Python, Ruby, JS, etc.) can do the same thing with their OR operator:

    b = list.next.to_s || "Reached end of list."

If list.next.to_s is non-nil, then the OR statement is short-circuited and list.next.to_s will be assigned to b. If b is nil and "Reached end of list." is non-nil, then OR statement will return the string literal to be assigned to b instead. Thus,

    a = b || c || 0

would be the equivalent for those languages.

edit: One BIG downside to this I forgot to mention at first: If nil and a false value are both possible for a variable, then this construction can betray you and break your heart.

Yup.

Personally, I like the ternary operator, and I also like the nil-coalescing operator, but I'm quite aware that they can produce difficult-to-maintain code, so I'm careful with them. I have gone and done some silly stuff with both, but then, I realized that I was leaving unmaintainable code.

If you use godbolt.org, you can actually see what code is produced by the source.

The second conditional is unneeded as the 0 will only be returned if c evaluates to 0, so it can equally well be written

    int a = b ?: c;

That's not specific to Objective-C, it's a GCC extension to the C language.