Hi, I know you already addressed a lot of the mischaracterization of Kon and Clark's relationship, but I was under the impression that Kon actually means 'abomination' in Kryptonian, and that Clark giving him that name was a rejection in itself. I am not very well versed in comics, so I apologize if this is just a fanon concept.
Hello!
You're not alone in being misled, as this concept has stretched far and wide and it is a very common theme in fandom works like fanfic.
The concept of Kon-El meaning "abomination" is canon, not fanon, but its source is from the New 52 reboot.
Some fans have in an attempt to create more angst for Kon adopted the concept that Clark gave Kon this name knowing full well what it meant as a way of rejecting him - this is incorrect - and it is blending versions together to make something that just never actually happened with Clark.
There are two versions of Kon getting his name in a main continuity - one in the 1994 comics, and the other in the New 52 Superboy comics.
To best answer your question, I am going to talk about the New 52 version first where "Kon-El" means abomination.
Also, it is important to remember that this Kon-El, isn't even actually Conner Kent (that's another post for another day comics are weird).
Anyway, in the New 52 reboot Superboy is 'called' Kon-El not by Clark, but by Kara!
Superboy v.6 (2011-2014) #6
In this iteration, Kara has some extreme prejudiced bigotry towards "Kon" for being a clone due to the disastrous history Krypton had involving clones. It prompted her to attempt to kill "Kon" the moment she found out he was a clone after more or less calling him a slur.
Superboy v.6 (2011-2014) #6
You can blame Scott Lobdell for this particular evisceration of Kara's character and for the name Kon-El warping into 'abomination' henceforth.
This particular run and story is no longer relevant to main continuity and it is not attached to Conner Kent because this did not happen to Conner Kent, but it did in fact happen and Krypton's disastrous history involving clones is still canon as well. Kon is still facing varying degrees of discrimination from Kryptonian-based ideology (Eradicator) because he is a clone.
Now let's talk about Clark and Kon and where Kon-El first came from and put a stop to the slander.
Where the name "Kon-El" originally came from was from Conner's 1994 solo series where Clark offered it to him from a place of affection.
Superboy (1994) #59
The original moment of Kon obtaining his name from Clark was profound because up until this point he did not have a proper name. He was just "Superboy" or "Kid" or "Pup" (derogatory) so when Clark offers this Kon is so happy he starts crying.
Superboy (1994) #59
At this point in time in comic history Kon-El did not mean abomination, "Kon" was a real Kryptonian name, and in the original run Clark did not even have any resentment towards Kon or negative feelings about his existence at all. He trusted him, felt he was worthy of the S-shield as a representative of hope, and at this point he wanted him to be part of his family.
This is Clark adopting Kon into his family right here in this moment - because Superman is the tale of the immigrant, the refugee and of love in family where blood does not equal family. That is what he is saying right here in this issue.
It is also important to note that at this point Geoff Johns' making Kon a 'clone' of Lex AND Clark is not canon and Kon is not even supposed to be blood related to Clark.
In closing...
Clark's relationship to Kon/Conner Kent in the main comic continuity is not hostile or rejection-based.
In their comic origins they had a nebulous relationship which over time evolved to being firmly brothers with a huge age gap and now in current continuity they are again brothers but with a different perspective.
Action Comics #1028
Current continuity Clark who doesn't remember Kon at all knows him for less than a week and claims him and he is actually distraught he doesn't remember him.
Fandom is transformative and angst/hostility/rejection will always be a major theme people will love to create and consume - but it is also important to recognize that some details are simply not canon and should be regarded as transformative works to tell a story.
I hope this clears some things up from the comics side of DC.
