As shown in the second bar of the third complete system (fourth system on the page), I guess it tells me to play like this on first/second time or something.
What is the name of notation? I searched Del Segno but it doesn’t seems right.
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It means that the very first time that measure is played, it's played with the non-parenthesized notation. On any subsequent visits to that measure, it's played according to the parenthesized notation.
There's no special name for this instruction, but it serves a similar purpose to writing separate "endings":
X: 1 T: First and second "endings" M: 4/4 K: Db clef=bass middle=D L: 1/8 G,G- G3/2A,/2- A, A2 F |1 F,F- F3/2B,/2- B,3E ||2,3,4 F,F- F3/2B,/2- B,4 ||