"וַיֹּאמֶר אַבְרָם ה"א מַה תִּתֶּן לִי וְאָנֹכִי הוֹלֵךְ עֲרִירִי וּבֶן מֶשֶׁק בֵּיתִי הוּא דַּמֶּשֶׂק אֱלִיעֶזֶר." (Gen 15,2)
"וְשֵׁם הָאֶחָד אֱלִיעֶזֶר כִּי אֱלֹהקי אָבִי בְּעֶזְרִי וַיַּצִּלֵנִי מֵחֶרֶב פַּרְעֹה." (Ex 18,4)
The Torah says nothing about why Avraham's slave was called Eliezer, but rather ascribes the explanation to Moses' son. (I titled it "after" not really "in respect to" but chronologically after).
Some questions arise:
Why the slave was called (all of sudden) Eliezer?
Moses should have known about Avraham's slave, did he call his son after him?
Those are the only two Eliezers in the Torah (there are some more in the Nakh) - what's the connection? Like Baal Haturim likes to draw parallels.