I believe it was already mentioned that "APTX 4869" is a wordplay on Sherlock Holmes's name.
I noticed now that you can also take Vermouth's two names, Sharon (シャロン Shi-Ya-Ro-N) and Chris (クリス Ku-Ri-Su), combined to form that same Shi-Ya-Ro-Ku. Coincidence? Maybe. Important? Probably not. (Except if the one that chose the name has something to do with Vermouth...) Regardless, I wanted to share my findings. Thanks.APTX 4869 is a pun on "Sherlock Holmes". 4869 can also be pronounced "Shi-Ya-Ro-Ku" (シャロク Sharoku), which translates into Sherlock. (http://www.detectiveconanworld.com/wiki ... ame_origin)
PS: Is there a difference between wordplay and pun? I use the former, because in my language (German) the term for it is literally "wordplay" translated. Through the internet I've got to know "pun" for something funny. Just random thoughts to lighten the mood
Edit: I just remembered, aren't there people who think that Vermouth is Karasuma's wife or daughter/descendant? (Explaining why she is the boss's favorite.) If that's the case, then they could have named her Sharon/Chris purposely, because he's a Sherlock Holmes fan (or his descendants). I always manage to fit things together, even if I don't believe in the theory myself