Since it was the angel that instructed Hagar to call her son by the name Yishmael, how come it was Avraham who named him (16:15)?
Ramban #2: Hagar, in her capacity as a concubine, felt uncomfortable to name her son formally, so she told Avraham what the angel had told her, and Avraham carried out the angel's instructions.
Seforno: The name Yishmael was appropriate from the point of view of Hagar, as the angel explained to her; and also with respect to Avraham, who later prayed to HaSh-m on his behalf (17:18), and HaSh-m answered favorably (17:20). 3
He should have been called Shama'el, "for HaSh-m heard (Shama) her affliction" (past tense)!
Moshav Zekenim: He was called Yishmael, for HaSh-m will hear his voice in the future [when he will be close to death from lack of water] (21:17).
"You shall call his name 'Yishma'el,' for HaSh-m has heard your affliction." Our sages write that HaSh-m made His name part of our name, Yisrael, so that we would never be lost among the nations. It seems from this verse, however, that His name is a part of Yishma'el's name as well?
Maharal (Netzach Yisrael, Ch. 10, p. 63): Yishma'el's name only tells us that HaSh-m heard the prayer of Hagar [but does not indicate a Divine relationship with the nation descended from her]. "Yisrael" means, "for you struggled [both] with the G-dly and mortals" (32:29); this shows a G-dly aspect in the nation itself. 1
Additionally, unlike in the name "Yisrael," the "Tzeirei" in Yishma'el's name is under the Ayin, while the Alef is silent; thus the name of HaSh-m is not fully pronounced (Ben Yehoyada to Megilah 18).
QUESTIONS ON RASHI
Rashi writes: "Hinach Harah [means] - when you return, you shall conceive [again]." But perhaps the angel refers to her existing pregnancy?
Gur Aryeh #1: Hagar had already miscarried the first pregnancy , due to the Ayin ha'Ra (Rashi to 16:5).
Gur Aryeh #2: Hagar would already be aware of her first pregnancy, and the angel would not have had to inform her of it.
Rashi writes: "[The verb] v'Yolad't is equivalent to v'Yoledes." What is Rashi explaining?
Gur Aryeh: We may have misinterpreted the verb as past-tense (v'Yalad't - "you gave birth"). Rather, it is in present tense, "You are giving birth [to a boy]."
Rashi writes: "v'Karas Shemo - this is a command." what is Rashi clarifying?
Gur Aryeh: Rashi demonstrates that the verb is a command, (despite that the Reish has a Kamatz, and the Alef is silent,) for we find a similar verb in 17:19.