Only because it uses names does not disqualify it from being a parable.
Yes, it absolutely does disqualify it as being a parable because of the reasons already given.
As I already asked, why would Abraham (and not God) be in charge of Hades?
First, why do you assume that Abraham is in charge of Hades? And second, God is in charge of Hades, for he created it.
To me it is clear that this parable represents the blessing of being poor, which Jesus mentioned in Matthew 5 & 6. I mean, please read the first 18 Verses of Luke 16. Jesus warns us that we cannot serve two masters. Taken in context, the situation with Lazarus and the Rich Man makes sense. The rich man served money and thought he could have everything, but eventually had nothing.
It is not clear even you force it to be a parable, for there is no way to rightly interpret it because there is no symbolism in it. For the most part, mainly those who have adopted the belief in soul sleep and annihilation interpret the rich man and Lazarus as a parable and that because it destroys there interpretation. When we read it in its plain literal meaning, it makes perfect sense:
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Now there was a rich man dressed in purple and fine linen, who lived each day in joyous splendor.
20And a beggar named Lazarus lay at his gate, covered with sores
21and longing to be fed with the crumbs that fell from the rich man’s table. Even the dogs came and licked his sores.
22One day the beggar died and was carried by the angels to Abraham’s side. And the rich man also died and was buried.
23In Hades, where he was in torment, he looked up and saw Abraham from afar, with Lazarus by his side.
24So he cried out, ‘Father Abraham, have mercy on me and send Lazarus to dip the tip of his finger in water and cool my tongue. For I am in agony in this fire.’
25But Abraham answered, ‘Child, remember that during your lifetime you received your good things, while Lazarus received bad things. But now he is comforted here, while you are left to suffer.
26And besides all this, a great chasm has been fixed between us and you, so that even those who wish cannot cross from here to you, nor can anyone cross from there to us.’
27‘Then I beg you, father,’ he said, ‘send Lazarus to my father’s house,
28for I have five brothers. Let him warn them so they will not also end up in this place of torment.’
29But Abraham replied, ‘They have Moses and the prophets; let your brothers listen to them.’
30‘No, father Abraham,’ he said, ‘but if someone is sent to them from the dead, they will repent.’
31Then Abraham said to him, ‘If they do not listen to Moses and the prophets, they will not be persuaded even if someone rises from the dead.’”
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v.20-21 - In its plain literal meaning, i.e. at face value, we are introduced to the rich man, with Lazarus being a poor beggar. That Lazarus was laid at the rich man's gate longing to be fed with the crumbs from the rich man's table infers that the rich man had no compassion on Lazarus.
v.22 - Both Lazarus and the rich man physically die, with Lazarus' spirit being taken to Abraham's side in Hades and the rich man's spirit going down into a the place of torment within Hades. The fact that the rich man could see Abraham and Lazarus by his side and that he complained that he was in agony, demonstrates that after both had died, their spirits were conscious and aware.
v.24 - The rich man cries out to Father Abraham to have mercy on him and send Lazarus to dip his finger in the water to touch the rich man's tongue being in agony in the flame. Just a note, just because the rich man asks for water, it does not mean that it would even do anything. The rich man may have just requested water because that is what he would have done when he was alive. The gist is that he is in torment in the flame and it can't be quenched.
v.25 - Abraham responds "remember that during your lifetime you received good things and Lazarus bad things" which would be referring to their lives before they had died. Now after death and their spirits being in Hades, their circumstances are reversed with Lazarus being in a place of comfort/paradise and the rich man left to suffer.
v.26 - Even if Lazarus could get some water for the rich man, Abraham tells him that there is a great chasm fixed between them separating the place of comfort from the place of torment, so that those in either location cannot cross over to one another. Which demonstrates that both areas were/are in Hades, but separated and unpassable.
v.27-28 The rich man then begs Abraham to send Lazarus back up to the earth to his father's house in order to warn his five brothers so that they would not come to the same place of torment.
v.29 - Abraham tells him that they have Moses and the prophets (word of God) to warn them from coming to that place of torment
v.30-31 Abraham tells him that if his brothers won't be warned and repent by the word of God, then they neither will they be persuaded to repent if someone rises from the dead, which was a hint at Jesus resurrection, meaning that, Jesus rose from the dead and people still not believe.
The rich man is there in Hades as I write this post and will remain there until he is resurrected out of Hades to stand before God at the great white throne judgment, along with all of the unrighteous dead throughout all of history.
If you will just read it in its plain literal meaning instead of forcing a parabolic interpretation on it, it makes perfect sense.
If the plain, literal sense makes good sense, then don't seek any other sense. In your case, you and others are ignoring the plain literal sense and forcing a parabolic interpretation on it, when there is no reason to apply that.
Just read it as it appears and you'll get it.