Can anyone tell me name of this opening where knight is sacrificed? Is there any way to take knight and save rook at same time?

Please do tell name, so I can search on YouTube.

 [FEN ""]

 1. e4 e5 2. Nf3 f6 3. Nxe5 fxe5 4. Qh5+
As Akavall said correctly, it is the Damiano Defense, and is named after Pedro Damiano (1480–1544).

Since he answered the basic question about the name, I would not normally, but there is an additional part to the question, so I am going to add that 2...f6? is virtually a forced loss, no matter how you play it, and here is the analysis. So, no you cannot take the knight, and save the rook, or worse happens.

 [FEN ""]

 1. e4 e5 2. Nf3 f6 3. Nxe5 fxe5 $2 (3... Qe7 4. Nf3 Qxe4+ 5. Be2 d5 6. O-O {And black is already dead on the e-file. The immediate threat is Bb5+ and Re1 winning the queen. The ugly Ne7 is the best move here.} Ne7) 4. Qh5+ Ke7 (4... g6 5. Qxe5+ Qe7 6. Qxh8 Qxe4+ 7. Kd1 $18) 5. Qxe5+ Kf7 6. Bc4+ d5 (6... Kg6 7. Qf5+ Kh6 8. h4 $1 Qe7 9. d3+ g5 10. hxg5+ Kg7 11. Bd2 d5 12. Bc3+ Nf6 13. gxf6+ {And mates in four.}) 7. Bxd5+ Kg6 8. h4 h6 (8... h5 9. Bxb7 Bd6 10. Qa5 Nc6 11. Bxc6 Rb8) 9. Bxb7 Bd6 (9... Bxb7 10. Qf5#) 10. Qb5 Nf6 11. Bxa8 $18