The Greek form Eliezer transliterates the Hebrew Eliezer (God is my help). It appears in Luke 3:29 in Jesus' genealogy. The most famous OT Eliezer was Abraham's servant (Genesis 15:2; 24) who sought a bride for Isaac — a type-scene of the Holy Spirit seeking the bride for the Son.
The name Eliezer (God is my help) encompasses the whole biblical theology of divine assistance. The unnamed servant of Genesis 24 — almost certainly this Eliezer — becomes one of the richest typological figures in the OT: sent by the father, traveling to a foreign land, seeking a bride for the son, giving gifts, and bringing her back. Early church fathers read this as a picture of the Spirit's work in calling the church (the bride) for Christ (the son). The name itself proclaims the theology: only God is our true help.