Why does the Torah refer to Dinah as "Bas Leah," and not 'Bas Yaakov'?
Rashi: Because, like her mother, 1 who "went out" to meet Yaakov (30:16), Dinah "went out" 2 to see the maidens of the land. 3
Ramban: To stress that she was the full sister of Shimon and Levi, who took the lead in avenging her honor.
Ohr ha'Chayim: The Torah gives the reasons that caused her to go out. (a) She was Bas Leah, who went out. (b) She was Yaakov's only daughter among his sons; being Bas Yaakov made her famous. (c) She went to see the local girls. Pirkei d'R. Eliezer (38) says that Shechem brought girls around Yaakov's tent to play with lyres, to entice her to come out.
Malbim: This teaches that Dinah did not breach modesty. She was Bas Leah, who was modest in her tent. "Asher Yaldah l'Yaakov" - her birth is attributed to Yaakov - she was modest and Kosher. She did not go out to see the boys, rather, to see the girls.
Ner Uziel (p. 210): Dinah, like Leah, had potential to fix Esav or other Resha'im. Leah married Yaakov, who received some of Esav's potential that through the Berachos intended for him. Dinah did not marry Esav, so she sought to fix Benos Shechem.
It is from here that the saying 'like mother, like daughter' arose.
Chochmah u'Musar (Vol. 2, p. 460): Leah went out for a Mitzvah, to beget a Shevet, and merited Yisachar. What is wrong with this?! It is because she took Rachel's Onah (time for intimacy). Even though Rachel consented, both of them were punished, it caused pain to Yaakov, and through the episode with Dinah, it was written about Shimon and Levi, "Kelei Chamas Mecheroseihem" (49:5) - all for a minor misdeed!
What is the significance of the fact that Dinah went out to see the maidens?
Oznayim la'Torah: We learn from Dinah that, when a person goes to see, he is also seen and one therefore needs to weigh-up whether it is worth going out. Otherwise, he may be forced to suffer the consequences.
Ha'amek Davar: Yaakov was outside the city. It should have said that she came! Rather, she 'went out' from the proper place.
After calling Dinah "Bas Leah," why does it add "Asher Yaldah l'Yaakov"?
Ramban: Because all Bnei Yaakov (even those from other mothers) displayed zealousness on her part to some degree.
Nidah 31a: Only Dinah is attributed to Yaakov, to teach that if the man is Mazri'a first, the child will be a girl.
Moshav Zekenim: The debacle was also due to Yaakov. He was punished for hiding her in a box (refer to 32:23:1:1 and the note there).
Ha'amek Davar: Due to Yaakov's importance, Shechem desired his daughter.
