"Don't know what the name is" vs. "Don't know what it's called"

For most listeners, the two examples will communicate the same thing, that speaker B doesn't know the name of meal #4. Technically, of course, B might know the name but not know what the name is or what the meal is called, etc. Here is a classic example, that illustrates several distinctions:

"Or else what?" said Alice, for the Knight had made a sudden pause.

"Or else it doesn't, you know. The name of the song is called 'Haddocks' Eyes.'"

"Oh, that's the name of the song, is it?" Alice said, trying to feel interested.

"No, you don't understand," the Knight said, looking a little vexed. "That's what the name is called. The name really is 'The Aged, Aged Man.'"

"Then I ought to have said 'That's what the song is called'?" Alice corrected herself.

"No you oughtn't: that's another thing. The song is called 'Ways and Means' but that's only what it's called, you know!"

"Well, what is the song then?" said Alice, who was by this time completely bewildered.

"I was coming to that," the Knight said. "The song really is 'A-sitting On a Gate': and the tune's my own invention." ...

Most of the time, to most listeners, "the name of the meal" and "what the meal is called" would be the same thing. There may sometimes be a difference if the meal has a formal name, but is often informally called something else.

This is more typical for a person, who might have the legal name John Smith, but is almost always called Jack (which is a standard variation on the name John). Only one is his name, but the other is "what he is called".