user1752: The position is analyzed in many endgame works, but to my knowledge hasn't been given a name as other similar endgames (e.g. "Vancura's position") have.
Two of the most authoritative works, Nunn (2008) and Dvoretsky (2011), don't give it a name or cite a first analyst. 
K7/P4k2/8/8/8/8/4R3/1r6 w - - 0 1

Dvoretsky, M. (2011). Dvoretsky's endgame manual. SCB Distributors.
Nunn, J. (2008). Secrets of rook endings.

user-1: Herb Wolfe's answer checks some of the books quoted by the poster -and some others- where this endgame was mentioned, but any particular name was assigned to the position, being just included at Lucena/Philidor chapters.
The analysis don't look very deep, that migth be the reason why it has not a huge interest on GM analysis.
This is how stockfish wins against himself with white:
[FEN ""]
[FEN "K7/P4k2/8/8/8/8/4R3/1r6 w - - 0 1"]

1. Rc2 Ke7 2. Rc8 Kd6 3. Rb8 Ra1 4. Kb7 Rb1+ 5. Kc8 Rc1+ 6. Kd8 Rf1 (6... Rh1 7. Rb6+ Kc5 8. Rc6+ Kd5 (8... Kb5 9. Rc8 Ra1 (9... Rh8+ 10. Kc7 Rh7+ 11. Kb8)) 9. Ra6) 7. Ke8 Ra1 8. a8=Q *

However white wins because of black's king position. If the king starts on e7, it is drawn because white's king can't get away from a-column:
[FEN ""]
[FEN "K7/P3k3/8/8/8/8/3R4/1r6 w - - 0 1"]

1. Rc2 Kd7 2. Rh2 Kc6 3. Rh8 Kc7 4. Rb8 Rd1
5. Rb2 Rd8+ 6. Rb8 Rd1

If it is black's turn, white wins in a similar way.
[FEN ""]
[FEN "K7/P4k2/8/8/8/8/4R3/1r6 b - - 0 1"]

1... Rb3 2. Rc2 Ke6 3. Rc8 Kd6 4. Rb8 Ra3 5. Kb7
Rb3+ 6. Kc8 Rc3+ 7. Kd8 Rh3 8. Rb6+ Kc5 9. Rc6+
Kb5 10. Rc8 Rh8+ 11. Kc7 Rh7+ 12. Kb8


user9025: I've looked in several books, including Nunn's earlier edition of Secrets of Rook Endings (1992), Muller and Lamprecht's Fundamental Chess Endings, and Silman's Complete Endgame Course.
None of them have give it a name or source, although Silman refers to it as a "Lucena" but notes that it's not a true Lucena, since it's a rook pawn. It does tend to get grouped together with the Lucena and Philidor positions and the bridge and Karstedt maneuvers.

1752: <p>The position is analyzed in many endgame works, but to my knowledge hasn't been given a name as other similar endgames (e.g. "Vancura's position") have.</p>

<p>Two of the most authoritative works, Nunn (2008) and Dvoretsky (2011), don't give it a name or cite a first analyst. </p>

<pre><code>K7/P4k2/8/8/8/8/4R3/1r6 w - - 0 1
</code></pre>

<p>Dvoretsky, M. (2011). Dvoretsky's endgame manual. SCB Distributors.<br>
Nunn, J. (2008). Secrets of rook endings.</p>
 -1: <p><a href="https://chess.stackexchange.com/questions/22216/does-this-rook-endgame-have-a-name-or-known-original-analyst/22256#22256"><strong>Herb Wolfe's answer</strong></a> checks some of the books quoted by the poster -and some others- where this endgame was mentioned, but any particular name was assigned to the position, being just included at Lucena/Philidor chapters.</p>

<p>The analysis don't look very deep, that migth be the reason why it has not a huge interest on GM analysis.</p>

<p>This is how stockfish wins against himself with white:</p>

<pre><code>[FEN ""]
[FEN "K7/P4k2/8/8/8/8/4R3/1r6 w - - 0 1"]

1. Rc2 Ke7 2. Rc8 Kd6 3. Rb8 Ra1 4. Kb7 Rb1+ 5. Kc8 Rc1+ 6. Kd8 Rf1 (6... Rh1 7. Rb6+ Kc5 8. Rc6+ Kd5 (8... Kb5 9. Rc8 Ra1 (9... Rh8+ 10. Kc7 Rh7+ 11. Kb8)) 9. Ra6) 7. Ke8 Ra1 8. a8=Q *
</code></pre>

<p>However white wins because of black's king position. If the king starts on e7, it is drawn because white's king can't get away from a-column:</p>

<pre><code>[FEN ""]
[FEN "K7/P3k3/8/8/8/8/3R4/1r6 w - - 0 1"]

1. Rc2 Kd7 2. Rh2 Kc6 3. Rh8 Kc7 4. Rb8 Rd1
5. Rb2 Rd8+ 6. Rb8 Rd1
</code></pre>

<p>If it is black's turn, white wins in a similar way.</p>

<pre><code>[FEN ""]
[FEN "K7/P4k2/8/8/8/8/4R3/1r6 b - - 0 1"]

1... Rb3 2. Rc2 Ke6 3. Rc8 Kd6 4. Rb8 Ra3 5. Kb7
Rb3+ 6. Kc8 Rc3+ 7. Kd8 Rh3 8. Rb6+ Kc5 9. Rc6+
Kb5 10. Rc8 Rh8+ 11. Kc7 Rh7+ 12. Kb8
</code></pre>
 9025: <p>I've looked in several books, including Nunn's earlier edition of <code>Secrets of Rook Endings</code> (1992), Muller and Lamprecht's <code>Fundamental Chess Endings</code>, and <code>Silman's Complete Endgame Course</code>.</p>

<p>None of them have give it a name or source, although Silman refers to it as a "Lucena" but notes that it's not a true Lucena, since it's a rook pawn. It does tend to get grouped together with the Lucena and Philidor positions and the bridge and Karstedt maneuvers.</p>
