That doesn't seem to work for a couple of reasons:
1. Satan isn't the only angelic being that was lost:
Luk 11:15 But some of them said, He casteth out devils through Beelzebub the chief of the devils.
Beelzebub (Satan) is the chief of devils.
2Pe 2:4 For if God spared not the angels that sinned, but cast them down to hell, and delivered them into chains of darkness, to be reserved unto judgment;
It would seem that these are just as lost as Satan.
2. If all souls are given to him, then Christ said that some would not ever know him:
Mat 7:21 Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but he that doeth the will of my Father which is in heaven.
Mat 7:22 Many will say to me in that day, Lord, Lord, have we not prophesied in thy name and in thy name have cast out devils? and in thy name done many wonderful works?
Mat 7:23 And then will I profess unto them, I never knew you: depart from me, ye that work iniquity.
If Satan is Apollyon and Apollyon means perdition then it seems that the son of perdition would be Satan. It is always shown in the singular, never plural. It seems there can only be one.
I don't think Apollyon means "perdition". If you look at the greek:
Apolluōn
ap-ol-loo'-ohn
Active participle of G622; a destroyer (that is, Satan): - Apollyon.
Note that Apollyon is the active participle of Strongs G622:
apollumi
ap-ol'-loo-mee
From G575 and the base of G3639; to destroy fully (reflexively to perish, or lose), literally or figuratively: - destroy, die, lose, mar, perish.
Perdition, on the other hand, is:
apōleia
ap-o'-li-a
From a presumed derivative of G622; ruin or loss (physical, spiritual or eternal): - damnable (-nation), destruction, die, perdition, X perish, pernicious ways, waste.
Apollyon and perdition are both thought to have derived from the same word, but "perdition" seems to have softer meaning.
But even if Apollyon means perdition, and Satan is Apollyon, the in a real sense Judas could be thought of as the "son of Satan", the son of perdition, because he did Satan's bidding:
Luk 22:3 Then entered Satan into Judas surnamed Iscariot, being of the number of the twelve.
In this age, there is only one unpardonable sin and as terrible as what Judas did....it wasn't that named sin. Also, Christ selected Judas for the deed, to accomplish what He came to earth for. And....Judas repented, whether or not it was a heart felt repentance I don't know.
When it comes to scriptural study, as Diego pointed out, you need to be careful about making assumptions based on the English translations of greek words.
Mat 27:3 Then Judas, which had betrayed him, when he saw that he was condemned, repented himself, and brought again the thirty pieces of silver to the chief priests and elders
Judas "repented" is this word:
metamellomai
met-am-el'-lom-ahee
From G3326 and the middle of G3199; to care afterwards, that is, regret: - repent (self).
This word is only used in 5 verses and most often means regret. Judas regretted what he did. He cared AFTER he did it. But there's a different word that's always used to describe the repentance that leads to life:
Act 2:38 Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
The "repent" here is:
metanoeō
met-an-o-eh'-o
From G3326 and G3539; to think differently or afterwards, that is, reconsider (morally to feel compunction): - repent.
This word is used 34 time and always to refer to Godly repentance.
If you don't have one you should invest in a good concordance. There is a freeware (well donation) bible software program called "E-Sword" that has many dictionaries and concordances all free.
I thank you my friend for bringing this up. It is making an interesting study.
That doesn't seem to work for a couple of reasons:
1. Satan isn't the only angelic being that was lost:
That is true, there are also the fallen angels but he is the only one named. Many will go into perdition and Judas could well be one of those but are there more than one "named" as the son of perdition?
2. If all souls are given to him, then Christ said that some would not ever know him:
Mat 7:21 Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but he that doeth the will of my Father which is in heaven. Mat 7:22 Many will say to me in that day, Lord, Lord, have we not prophesied in thy name and in thy name have cast out devils? and in thy name done many wonderful works? Mat 7:23 And then will I profess unto them, I never knew you: depart from me, ye that work iniquity.
But because He will tell them, depart from Me, ye that work iniquity, doesn't mean they weren't given to Him.....it is that they didn't accept the salvation He offered. They were His but they refused Him.
But even if Apollyon means perdition, and Satan is Apollyon, the in a real sense Judas could be thought of as the "son of Satan", the son of perdition, because he did Satan's bidding:
Luk 22:3 Then entered Satan into Judas surnamed Iscariot, being of the number of the twelve.
You have hit upon the sticking point in the debate. I agree about the repentance of Judas and only our Father knows how much weight it will carry.
So, even though Judas did the bidding of Satan could he be considered THE son of perdition?
11 Thess.2:3 Let no man deceive you by any means: for that day shall not come, except there come a falling away first, and that man of sin be revealed, the son of perdition.
John 17:12 While I was with them in the world, I kept them in Thy name: those that Thou gavest Me I have kept, and none of them is lost, but the son of perdition; that the scripture might be fulfilled.
We know that Satan has been condemned and we know that his fallen angels have also been condemned but no one human has yet been condemned. Are the humans those that Thou gavest Me...and none of them is lost? Of course then one would say....but Satan wasn't human.....Oh gosh, I don't know. It is a prickly problem.
I just continue to hold on to him being named THE son of perdition, not A son of perditon or SONS of perdition.
I thank you my friend for bringing this up. It is making an interesting study.
It is that....and I thank you for your thoughts.
......Ping