I think I'm becoming a regular necromancer for this thread
1. No King of Númenórean descent after the foundation of Arnor and Gondor ever took the name Elendil.
2. The Steward Cirion's son, Hallas, came up with the name the Kingdom of Rohan, when it was given to Eorl and the Eotheod.
3. The term for "Regent" in Quenya, referring to a royal descendent exercising the King's authority on his behalf, is given as "Karma-Kundo" meaning "seat-guardian," and can more generally be translated as "Guardian of the Throne."