Twitter is not only ‘X’ on its own website. It’s ‘X’ on the App Store as well.
Up until today, while the logo for Twitter changed to ‘X’ on its website and its icon on the App Store and Google Play Store, the app was still called “Twitter” on Apple’s App Store. That changed today and now, the app is officially called ‘X’ — even on the App Store.
Apple usually requires that apps do not have a single character name on the App Store, so X seems to have worked with the company to get special permission to change its name.