Would it not suffice to say "Yehudah"? Why did Yaakov need to add, "Atah"?
Rashi: When Yehudah heard his father rebuke his three older brothers, he was afraid that also he would be rebuked (about the incident with his daughter-in-law Tamar), and he began to move away (toward the exit). That was when his father appeased him with warm words, intimating that he was different than they. 1
Seforno, Malbim: Yaakov was informing Yehudah that, unlike his three older brothers, he was worthy to take over the kingship, since, unlike them, there was nothing in him that prevented it.
Ohr ha'Chayim: The Berachos to the other brothers are for the distant future, after they enter Eretz Yisrael. But you yourself, Yehudah, your brothers will praise you - "Yehudah Gavar b'Echav" (Divrei ha'Yamim I 5:2).
Gur Aryeh: Rashi interprets this way due to the added word "Atah," which would otherwise be superfluous.
Why indeed, did Yaakov decline to rebuke Yehudah for his sin?
Targum Onkelos and Targum Yonasan: He earned a blessing in place of a rebuke because he did Teshuvah by admitting to Tamar. 1
Targum Yonasan: Which is why his brothers would acknowledge him (as their leader),Yisrael would come to be known as Yehudim, and why he would defeat his enemies, as the Pasuk goes on to state. (Moreover, he told him, that is why he was called 'Yehudah' (see Rashi to Divrei ha'Yamim I 16:11)).
What did Yaakov mean when he said, "Atah Yoducha Achecha!"?
Targum Yonasan: Refer to 49:8:2:1*.
Rashbam: He meant that Yehudah's brothers would grant him the majesty (Hod) 1 of kingship. 2 Malbim - This is like the Pasuk, "Al Ken Amim Yehoducha" (Tehilim 45:18).
Da'as Zekenim #1, Hadar Zekenim: They will admit that you are king over them.
Da'as Zekenim #2: All of Yisrael will be called Yehudim, from your name, and Mashi'ach will come from you.
As in Bamidbar 27:20 (See Rashbam, who gives other examples).
As is evident from the end of the Pasuk.
What does "Yadcha b'Oref Oyevecha" mean?
Targum Yonasan: It means that he will shoot arrows after them when they turn around (showing him the back of their necks) and flee.
Targum Onkelos: He will show a strong hand against his enemies, who will scatter and flee, turning the back of their necks to him. 1
Hadar Zekenim: When Esav wanted to kill [Yehudah's] brothers, Yehudah did not want to kill him from the front, for Esav's face resembled Yaakov's. 2 Rather, he killed him from the back. 3
Ohr ha'Chayim: When your hand is on the back of your enemies' necks, "your brothers will bow to you." This was in the days of Sha'ul, when David had the great victory on the back of his enemies' necks, Yisrael made him king over them. 4
Malbim: This is one condition for kingship - "u'Shefatanu Malkeinu... v'Nilcham Es Milchamoseinu" (Shmuel I 8:20). Also refer to 49:8:151:1.
Rashi: This was fulfilled in the days of David ha'Melech, who said "ve'Oyevai Tatah Li Oref" (Shmuel II 23:41). (Also refer to 49:8:4.1.)
Refer to 25:23:151.1
Hadar Zekenim: A Midrash of Chanukah says that there were decrees specifically against Shevet Yehudah, because Edom had a tradition that it was Yehudah who had killed their ancestor Esav. This is unlike the Midrash that Chushim ben Dan killed him at Yaakov's burial (Refer to 27:45:3:1* and 50:13:1:1*).
Ohr Yakar: In Shmuel II 5:1-2. (This was after the death of Sha'ul and Ish Boshes ben Sha'ul. Perhaps Ohr ha'Chayim means that David's victory was in the days of Sha'ul. - PF)
When Yitzchak blessed Yaakov (27:29), he referred to his maternal brothers ("Bnei Imecha"). Why, when Yaakov blesses Yehudah, does he refer to his paternal brothers ("Bnei Avicha")?
Rashi and Rashbam: Because, whereas Yitzchak had only one wife, Yaakov had four. 1
Gur Aryeh (to 27:29): But what about the reverse; why didn't Yitzchak say as Yaakov now did - 'the sons of your father'? Refer to 27:29:4.1.
What is the significance of "your fathers' sons will bow to you"?
Malbim: One condition for kingship is to judge the nation (refer to 49:8:4:5). This shows that they will accept his judgments.
Ha'amek Davar: Sometimes a Gibor can defeat his enemies, but he cannot conduct kingship amidst his brothers; sometimes it is opposite. You have both attributes - therefore they will bow to you.
How did Yehudah merit this blessing?
Maharal (Nesivos Olam, Nesiv Ahavas Hashem Ch. 2, p. 46): Descendants of Yehudah would later sanctify Hashem's name in public (at the Yam Suf); as such they received a blessing evident to all. 1
Maharal (Ohr Chadash p. 110, to Esther 2:5): Yehudah is the 'head' of Am Yisrael, as per our verse, "your hand is upon the back of the neck of your enemies;" as well as the verse, "Yehudah shall ascend at the head" (Shoftim 1:2). Also see Maharal (Gevuros Hashem Ch. 42, p. 159).
QUESTIONS ON RASHI
Rashi writes: "Your hand is upon your enemies' back-of-the-neck (Oref) - ... in David's time; as it says, 'My enemies You have given to me [by the] Oref' (Shmuel II 22:41)." When else might this verse be referring to?
Maharal #1 (Ohr Chadash p. 110, to Esther 2:5): Mordechai has descent from Yehudah; 1 Hashem set him in place (in Shushan) to overpower the enemies of Am Yisrael.
Maharal #2 (Chidushei Agados Vol. 2, p. 53, to Sotah 13a): When Esav later tried to prevent Yaakov's burial, Yehudah killed Esav from behind. (He did so because in front, Esav's face resembled that of Yaakov.) 2
Maharal #3 (Chidushei Agados Vol. 4, p. 55, to Avodah Zarah 25a): In warfare, one aims an arrow at the enemies' [retreating] neck. The bow and arrow is hard and swift, and strikes the target despite without direct contact (unlike the sword). As it lacks physical contact, it is more associated with the spiritual - an appropriate metaphor for Yehudah.
