Why does it say "Anah"?
Rashi: It is an expression of answering and screaming. We learn from "v'Anu ha'Leviyim" (Devarim 27:14).
Rashi (13, from Shir ha'Shirim Rabah 2:23): Anah was via Moshe; Amar was via Aharon.
Malbim (Melitzah): This is from afar. Later, "v'Amar" - He spoke privately, from nearby. Speech is elevated based on the preparation beforehand. First "Anah" from afar - He told her to prepare herself [to hear] Divine speech.
Why does he say to rise?
Rashi: "A'aleh Eschem me'Ani Mitzrayim" (Shemos 3:17).
Rashi (13, according to the metaphor): Make yourself zealous, "v'Yish'alu Ish me'Es Re'ehu" (Shemos 11:2).
Seforno: He aroused Yisrael amidst their slavery in Egypt, and told everyone to cast off the abominations of his eyes.
Until now, she was called just Rayasi. Why does it now add "Yafasi"?
Malbim (Melitzah): The bond of Rei'us (friendship) is due to choice. Love due to beauty is due to the beloved and his attribute of beauty. Once Ru'ach [Hashem] came on him once, He saw that she is beautiful, and proper to dwell in His Chatzeros and be satiated from the good of His house.
Where did he tell her to go?
Rashi (13, according to the simple meaning): A youth entices his betrothed to go after him. So my Beloved did to me.
Malbim (Melitzah): He told [Shlomo's Nefesh] to leave Chadrei Shlomo (the body).