John Chrysostom

But a parable is that in which an example is given, while the names are omitted. Lazarus is interpreted, "one who was assisted." For he was poor, and the Lord helped him.

Catena Aurea by Aquinas ↗

Theophylact of Ohrid

And He mentions the poor man by name, for the names of the righteous are written in the book of life. It is said, according to the tradition of the Hebrews, that at that time there was in Jerusalem a certain Lazarus who was in extreme poverty and sickness, and that the Lord mentioned him, taking him into the parable as someone manifest and well-known. The rich man was in every respect prosperous. He was clothed in purple and fine linen, and not only was he clothed, but he also enjoyed every other pleasure. …

Commentary on Luke ↗

Ambrose of Milan

This seems rather a narrative than a parable, since the name is also expressed.

Catena Aurea by Aquinas ↗

Gregory the Dialogist

And whom does Lazarus full of sores figuratively represent, if not the Gentile people? For when he turned to God and was not ashamed to confess his sins, he had a wound on his skin. For in a wound of the skin, poison is drawn from the inner parts and bursts forth outward. What then is the confession of sins, if not a kind of breaking open of wounds? For the poison of sin is healthfully opened in confession, which was festering within the mind. For wounds of the skin draw the fluid of corruption to the surface. …

Forty Gospel Homilies, Homily 40 ↗

Bede

And there was a certain beggar named Lazarus. Certainly in the populace it is more common for the names of the rich rather than the poor to be known. Why is it then that the Lord, when making a parable about a poor man and a rich man, mentions the name of the poor man, but does not mention the name of the rich man, except that God knows the humble and approves of them, and disregards the proud? …

On the Gospel of Luke ↗