First of all, i confirm that アフター does stand for "after party" (though Muyu misuses the slang).
Regarding "Ao Tita" it's obviously a short for the longer name we can see on the gacha machine.
It reminds me of "Blue Archive" for some reason which is shortened into ブルアカ (Blue Aka) in japanese.
if i had to translate, i would go with "Blue Titan" because it sounds more natural to me to shorten it that way if it were to be adapted into english.
Thank you for spotting some light on this manga which i like a lot !!