"X" feels (to me) much more ambiguous than "Twitter".
If you say "Twitter", people know what you're talking about. If you say "X", are you talking about "X" marks the spot? Rated "X"? "X" the former project name for Paypal? "X" as in an unknown quantity? "X" is used in a lot of different contexts. I think if you want to use the name "X", then you should probably say "The company, X,".
Twitter is a verb, but when you use it as a noun, the listener instantly knows that you are talking about the company "Twitter". Plus, it's the name we are all familiar with.