"Then gathered the chief priests and the Pharisees a council, and said, What do we? For this man doeth many miracles. If we let him thus alone, all men will believe on him: and the Romans shall come and take away both our place and nation. And one of them, named Caiaphas, being the high priest that same year, said unto them, Ye know nothing at all, nor consider that it is expedient for us, that one man should die for the people, and that the whole nation perish not. And this spake he not of himself: but being high priest that year, he prophesied that Jesus should die for that nation; and not for that nation only, but that also He should gather together in one the children of God that were scattered abroad. Then from that day forth they took counsel together for to put Him to death" (Jn. 11:47-53).
On the other side of the coin, the death of Lazarus seems to have been viewed by the Gospel writers as being of less importance than the preaching of John the Baptist, the feeding of the 5000, the Lord's anointing by Mary, the Last Supper, and Peter's denials, etc., all of which are recorded in each of the four Gospels. Only John records the raising of Lazarus, and his relationship to Mary and Martha (Jn. 11:1 - 12:19). In addition, Luke wrote about Mary and Martha, the sisters of Lazarus, but failed to mention him, even indicating that the house belonged to Martha (Lk. 10:38-42).
Which brings me the Lord's discussion of "the rich man and Lazarus" in Luke 16:19-31. Few, if any, have suggested that the "poor" Lazarus as described in Luke's Gospel, and the brother of Mary and Martha were the same man. I hesitate to do so here, because my suggestion might add support to those who insist Luke 16:19-31 is a parable. Of that, I am certain it is not! That being said, could the "economic status" of the rich man and Lazarus be a picture of the spirituality of the Pharisees and of Lazarus? Remember the actual parable of the Pharisee and the Publican praying; the Pharisee was "rich" outwardly but "poor" spiritually, while the Publican was "poor" in the eyes of men, but "rich" in the eyes of God (Lk. 18:9-14). I will tell you this: there are former "high priests" in torment today as they await God's certain judgment, while there are millions of humble sinners basking in the presence of our Lord at this very moment!
Does it make a difference if there were two individuals named Lazarus?
No. The real question is, with which Lazarus do you identify?