"What B" as a shortening of "What word starting with the letter B"

What B....? is used on gameshows like Weakest link and BBC Tv QI rather than

"What thing beginning with B....? or

"What proper noun beginning with...?"

because the answer required is not directly the word; the question is asking for a proper noun as the answer. It's just a way of making the program move more quickly / reduce the amount of time it takes to ask the questions. I'm not sure of a name for this other than 'abbreviation' or 'expediency'.

If the show start with an explanation of the rules, fully explaining what's required, then the actual posing of the questions is a form of ellipsis:

[Cambridge Dictionary]
Ellipsis happens when we leave out (in other words, when we don’t use) items which we would normally expect to use in a sentence if we followed the grammatical rules. …
In fact, when we use ellipsis appropriately, no one thinks we have ‘left out’ anything, and ellipsis is normal and very common, especially in informal conversation. …

---

For example, at the start of the show:

I'll ask you a series of questions about words that start with a certain letter.

During the show:

What [word that starts with] B was the name of the first lunatic asylum in Europe and is also a slang word meaning chaos? Bedlam.

In that scenario, the words in square brackets are left out because the meaning is understood—and it would likely be repetitive if they were said every time.