From the experts:
Eleazar is a distinguished Biblical name--in which it appears several times-- ripe for the picking following the stardom of Eli, Elijah, and other similar names.
Eleazar is also a Twilight name, first appearing in the Stephenie Meyers book Breaking Dawn.
It's related most closely to Eliezer, which also appears in the Bible many times. The name also belonged to three great Talmudic scholars.