As Paul D. Waite pointed out in the comments, this answer deals with your question quite handily.
Wagon Train, a popular western, would have had quite an easy trademark case against the show if it had so blatantly used a name derived from it. They could have easily argued that any success of the space show derived in part from the explicit tie to their popular Western. Similarly, if the space show fared poorly they could argue the same link damaged their show.
Therefore, it was completely impractical to call the show Wagon Train to the Stars. Even if it had been practical from a legal standpoint, the name is too long. Most shows have snappy, 1-3 word titles. Those which don't have easy titles don't find themselves being discussed as often - people will just talk about a show called Glee more than they would Singing Teenagers With Social Issues.
The word Trek mean to travel or explore. It's not in common usage, even at that time, so it tends to stand out in people's minds. The word Star, of course, indicates that the show deals with space. At the time, when the Space Race was on, space was HUGE (which is why a 'Western, in space' was such an appealing concept).
Thus, Star Trek was chosen as a superior name. I do not know who originally thought up the name, but once they did, I expect it stuck quite quickly.