Aria
Can I say "This sentence is called a X" instead of "This sentence is what's called a X"?

Yes, you can say "This sentence is called a mnemonic device" instead of "This sentence is what's called a mnemonic device". "This sentence is actually what’s called a mnemonic device" is written this way to make the sentence more interesting, but "This sentence is called a mnemonic device" has the same meaning.