Does this rook endgame have a name or known original analyst? 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.
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.