It's not a great name because X does a poor job of disambiguating what you're talking about. "Twitter" is unambiguous almost always, unless you're talking about bird vocalizations in a colloquial way, and it allows the verb form "tweeted". When it's clear from context (it often is), then "X" is fine, but you lose the verb ("Xed" means crossed out), and in a fair number of contexts it's ambiguous (e.g. "I like X"--do you mean the letter, is it an analogy to algebra, is the social media site, etc.?).

So, the social media site X may officially call itself "X" but as a practical matter its full name has to be "the social media site X" or "X (formerly known as Twitter)".