The phrase דמשק אליעזר first appears when Avram laments that his heir apparent is Eliezer, the steward of his household (Bereishit 15:2), and this same Eliezer later reappears as the trusted senior servant sent to find a wife for Yitzchak (Bereishit 24:2-9).
Chazal read "דמשק" not geographically but homiletically: Yoma 28b:8 teaches that Dammesek is a contraction of doleh u'mashke — one who draws and gives drink to others from his master's Torah — meaning Eliezer had mastered and disseminated Avraham's teachings, a reading Rashi (Bereishit 15:2) cites directly, alongside the Targum's and midrashic sense that Eliezer experienced miracles "at Damascus" (Targum Jonathan on Bereishit 15:2, Midrash Lekach Tov, Bereishit 15:2:2, Midrash Aggadah, Bereishit 15:2:2).
Other rishonim take the name more literally or etymologically: Chizkuni (Bereishit 15:2:2) identifies him as born in Damascus and a grandson of Nimrod, while Shadal (Bereishit 15:2:5) analyzes whether "Dammesek" and "Eliezer" form one compound name or two, rejecting Ibn Ezra's reading and favoring that Dammesek was an original name to which Eliezer was added.
Bereishit Rabbah develops Eliezer's character as mirroring Avraham's own virtue — his very visage resembled his master's, and he ruled over his own inclination as Avraham did (Bereshit Rabbah 59:8) — and elsewhere groups him with Moshe and Shlomo as one of three whose words were answered the instant they finished speaking (Bereshit Rabbah 60:4).
Later commentators probe Avraham's motives in sending Eliezer and the oath he imposed: the Sforno and Or HaChaim both explain that Avraham's age and wealth made him suspicious that Eliezer might seek to marry his own daughter into the family, hence the stringent oath regarding Canaanite wives (Sforno on Bereishit 24:1, Or HaChaim on Bereishit 24:1), and Rashi (Bereishit 24:39) records that Eliezer indeed had a daughter he hoped to match with Yitzchak, which Avraham rebuffed.
The Kli Yakar reads "ha-moshel be-khol asher lo" as possibly referring to Eliezer's mastery over his own wealth rather than Avraham's, distinguishing one who rules his possessions from one ruled by the desire for money (Kli Yakar on Bereishit 24:2).
On Eliezer's test for a worthy wife, Rashi, the Ramban, and the Sforno all treat his words "otah hochachta" as a petition rather than divination, clarifying that Eliezer prayed for a sign rather than relying on omens (Rashi on Bereishit 24:14, Ramban on Bereishit 24:14, Sforno on Bereishit 24:14), a point the Alshekh extends by explaining why the verse attributes the choice to Yitzchak specifically, since Yitzchak's trait was to exceed what was asked of him, so Eliezer sought a wife who would likewise give more than requested (Alshekh on Torah, Bereishit 24:8).
The Ramban also discusses Eliezer's conduct upon arrival, noting that he loosened the camels' harness-ropes and that, following the model of Rabbi Pinchas ben Yair's donkey which required no safeguarding from forbidden food, Avraham's camels certainly needed no such caution since no harm befalls a tzaddik (Ramban on Bereishit 24:32).
Chassidic sources find in Eliezer and Dammesek a symbol of spiritual service: the Sefat Emet links doleh u'mashke to the mode of service that preceded Avraham's circumcision, a stage of avdut akin to derech eretz which came before Torah (Sefat Emet, Bereishit, Chayei Sara 11:4), and elsewhere frames Eliezer's plea of chesed as rooted in Avraham's own primary attribute (Sefat Emet, Bereishit, Chayei Sara 28:4), while the Shem MiShmuel's discussion of Sarah's death touches tangentially on the Akeidah narrative surrounding this same chapter (Shem MiShmuel, Chayei Sara 1:2).
The kabbalistic reading found in Valle takes "Dammesek" as an allusion to the klippah, explaining that its placement before Eliezer's name in the pasuk hints at the klippah's hold over him owing to his impure root, a theme repeated in both his treatment of Bereishit 15 and of Bereishit 14 (Valle on Bereishis 15, Valle on Bereishis 14).
