user15478: Do any books or other resources discuss this variation for Black? Does it have a name?
The general idea is to go 4...h6, then ...d6 and ...g5 in some order, depending on what White does.
S. Mamedyarov plays this line a lot.
Sample line:
 [FEN ""]
    1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. d3 h6 5. c3 d6 6. O-O g5


user924: FM Andrey Terekhov's Two Knights Defense repertoire on Chessable uses this variation against 4.d3.
That repertoire deserves to be more widely known: it's one of the best on Chessable, the author updates it frequently, and it's free!
In the introductory text of 4.d3 h6 he notes:

In the beginning, this line has been mostly used as a surprise weapon, but in the past two years it developed its own body of theory. GM Alexey Kuzmin published a couple of articles summarizing the latest developments in this line in "ChessBase Magazine" (in 2018) and in Russian "64" (2019) .

So those are sources too.
And according to a ChessPub discussion, there are also two analyzed games in this line in Alexander Ipatov: Unconventional Approaches to Modern Chess Volume 1; Thinkers Publishing 2019, although I don't see it in that book's list of contents.

15478: <p>Do any books or other resources discuss this variation for Black? Does it have a name?</p>
<p>The general idea is to go 4...h6, then ...d6 and ...g5 in some order, depending on what White does.</p>
<p>S. Mamedyarov plays this line a lot.</p>
<p>Sample line:</p>
<pre><code> [FEN &quot;&quot;]
    1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. d3 h6 5. c3 d6 6. O-O g5
</code></pre>
 924: <p>FM Andrey Terekhov's <a href="https://www.chessable.com/book.php?bid=18646" rel="nofollow noreferrer">Two Knights Defense repertoire on Chessable</a> uses this variation against 4.d3.</p>
<p>That repertoire deserves to be more widely known: it's one of the best on Chessable, the author updates it frequently, and it's free!</p>
<p>In the introductory text of 4.d3 h6 he notes:</p>
<blockquote>
<p>In the beginning, this line has been mostly used as a surprise weapon, but in the past two years it developed its own body of theory. GM Alexey Kuzmin published a couple of articles summarizing the latest developments in this line in &quot;ChessBase Magazine&quot; (in 2018) and in Russian &quot;64&quot; (2019) .</p>
</blockquote>
<p>So those are sources too.</p>
<p>And according to <a href="https://www.chesspub.com/cgi-bin/chess/YaBB.pl?num=1568098530/12" rel="nofollow noreferrer">a ChessPub discussion</a>, there are also two analyzed games in this line in Alexander Ipatov: <em>Unconventional Approaches to Modern Chess Volume 1</em>; Thinkers Publishing 2019, although I don't see it in that book's list of contents.</p>
