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