The X was originally used as the emblem for a short-running podcast about Tesla run by Mr Merritt, which stopped in February 2022.
Mr Merritt sent Mr Musk an animation featuring the logo, saying: “Do whatever you want with it.”
He added the original font had been found by his fellow podcaster Alex Tourville, an engineer. Mr Tourville said on Twitter: “At least I’m getting screwed by [Elon Musk].”
Mr Musk has previously said he wants to turn Twitter into “X, the everything app” and add new features such as payments.
Twitter chief executive Linda Yaccarino said: “X is the future state of unlimited interactivity – centered in audio, video, messaging, payments/banking – creating a global marketplace for ideas, goods, services, and opportunities. Powered by AI, X will connect us all in ways we’re just beginning to imagine.”