In scripture names have very significant meanings. For example, the name Yeshua, means "YHVH delivers", which is why the angel said, "for he shall deliver his people from their sins", after revealing what the name of Christ would be. And in relation to this, the significance of the meaning of names, a name was used in this parable to convey a truth behind the meaning of the name Lazarus. If you do your homework, you will come to find that Lazarus is the Greek name for the Hebrew name Eliezer, who was a servant in the household of Abram. This is not a coincidence. Because what the parable is trying to convey is that Eliezer, who was not to be Abram's heir,
And Abram says, Master, O LORD, what will you give to me, for I am wasting away childless, but the son of Masek of my native-born maid servant, this Damascus Eliezer is heir? (Genesis 15:2 [ABP])
Then the word of the LORD came to him: “This man will not be your heir, but a son who is your own flesh and blood will be your heir.” (Genesis 15:4 [NIV])
Inherited the promises of Abraham, whereas the rich man, who was Jewish, which is why he calls Abraham father,
So he called to him, ‘Father Abraham…’ (Luke 16:24 [NIV])
Did not, even though it was unto the Jews that the promises of Abraham were given to. Its because these two men symbolize two types of people, the Jews, who had Abraham as father, along with the Law and the Prophets, which is symbolized by the rich man, and then the Gentiles, who were alienated from the promises of the Jews, which was symbolized by Lazarus/Eliezer,
Therefore, remember that formerly you who are Gentiles by birth and called “uncircumcised” by those who call themselves “the circumcision” (which is done in the body by human hands)– remember that at that time you were separate from Christ, excluded from citizenship in Israel and foreigners to the covenants of the promise, without hope and without God in the world. (Ephesians 2:11-12 [NIV])
Know then that it is those of faith who are the sons of Abraham. And the Scripture, foreseeing that God would justify the Gentiles by faith, preached the gospel beforehand to Abraham, saying, “In you shall all the nations be blessed.” (Galatians 3:7 -8[ESV])
Now if we are children, then we are heirs–heirs of God and co-heirs with Christ, if indeed we share in his sufferings in order that we may also share in his glory. (Romans 8:17 [NIV])