MT was firstly named "Primitive Twisted Generalized Feedback Shift Register Sequence" by a historical reason.
Makoto: Prof. Knuth said in his letter "the name is mouthful."

a few days later
Makoto:Hi, Takkun, How about "Mersenne Twister?" Since it uses Mersenne primes, and it shows that it has its ancestor Twisted GFSR.
Makoto:It sounds like a jet coaster, so it sounds quite fast, easy to remember and easy to pronounce. Moreover, although it is a secret, it hides in its name the initials of the inventors.
Makoto:Come on, let's go with MT!
Takuji:....well, affirmative.

Later, we got a letter from Prof. Knuth saying "it sounds a nice name." :-)