Keep in mind that you do not have to eat it, if it will put such a strain on you.
And you are not alone in this, there are a lot of private chicken keepers that would not even be able to butcher their birds and this is o.k. as well.
This will surely be more problematic when only raising a few birds, so you will get more attached when handling them.
And it was your first time ever, so be patient with yourself and don't try to force it.
I know of poultry breeders that even after more than 30 years of poultry keeping still...
Well, although they might not have 'normal' names, when dealing with them on a daily basis one often comes up with "the wild one", or "the friendly one" etc., so in your mind they will not be officially named but named nonetheless. ;)
What also helps is to be clear from the start that they will...
To prevent any of the above you could just keep them in the freezer for some more weeks or even month to give your mind time to adjust.
I found it much easier when there are several birds butchered at a time and letting them rest in the freezer for some months creating some kind of anonymity...