🔼The name Esli in the Bible
The name Esli (or Hesli, according to the New American Standard Bible) occurs only once in the Bible, namely in the genealogy of Jesus according to Luke (Luke 3:25), who traces Jesus ancestry through Nathan, son of David, whereas Matthew goes through Solomon and doesn't mention Esli.
🔼Etymology of the name Esli
The name Esli is probably a Greek transliteration of the Hebrew name אצלי (which doesn't occur in Old Testament) and comes from the preposition אצל ('esel), meaning reserved:
The final -i of our name comes from the Hebrew letter י (yod), which either create an adjective (reserved-like), a possessive form (my reservation), or may be a remnant of יה (Yah), which is short for יהוה, which is the name YHWH, or Yahweh.
For a meaning of the name Esli (Hesli), NOBSE Study Bible Name List appears to go with the adjective and reads Reserved. Spiros Zodhiates (The Complete Wordstudy Dictionary of the New Testament) sees a remnant of the name of the Lord and proposes Reserved By Jehovah.