🔼The name Addi in the Bible
The name Addi occurs only once in the Bible, namely in Luke 3:28, where it is applied to the great-great-great-grandfather of Zerubbabel, who was an ancestor of Jesus of Nazareth. The genealogy of Matthew doesn't mention this Addi because Matthew' lineage of the Christ goes through Solomon and Luke goes through Nathan.
🔼Etymology of the name Addi
The name Addi most probably derives from any of the following verbs:
For a meaning of the name Addi, NOBSE Study Bible Name List reads My Witness (taking it from the verb עוד, 'ud). Spiros Zodhiates (The Complete Wordstudy Dictionary) confirms our name is the same as Iddo but offers no translation of either.