What do you think came first, the name or the acronym?
Or if I'm misunderstanding your question: the network already existed due to that name because they already had all the right of way for the same reason UP did.
IIRC (it was a while ago) MCI came first and some VP at the SP was inspired by that to try to provide external service over their existing resource. After all they were in the transport business with a big infrastructure setup, so transporting bits was pretty natural.