I'm not sure why he thought of it, but a trek is a long, difficult or adventurous journey. It took on that meaning during the Boer migration into South Africa (it was originally a Dutch word meaning to draw or pull, as in to pull a wagon), and so I'd imagine it came to be associated with the mythology of the frontier, with grand pioneering quests and arduous adventures. Roddenberry gained a lot of his prior TV experience writing Westerns -- which were a ubiquitous part of TV culture at the time -- so the term "trek" and its frontier associations were probably somewhat prominent in his awareness. So I guess when he decided to do a show about pioneers journeying into the frontiers of space -- especially one that he pitched as "Wagon Train to the stars," in reference to a famous, successful Western series whose format he wanted to emulate -- Star Trek made sense to him as a title.
I wonder what the show would have looked like if they kept to the concept of wagon train to the stars? For one there was very little settlement in Star Trek, the show was about explorers not settlers. If it was to keep true to the wagon train concept it should have been about a number of families wanted to settle on a planet, they sell everything they had to purchase tickets on a starship to take them to a frontier planet so they can establish themselves, it would have been a very different Star Trek than the one we are familiar with, it would be about those families and not about a captain and his crew exploring various planets. I think the show Lost in Space was closer to the concept of Wagon Train to the Stars that Star Trek was.
Star Trek and Lost in Space are actually siblings, they both descend from the same movie Forbidden Planet. Lost in Space take the flying saucer and the Robot, gives it another top, and replaces the Crew in Forbidden Planet with a Family, the Family is a science fiction version of the Swiss Family Robinson, and instead of being marooned on an Island, they are marooned on a planet. Star Trek by contrast takes the paramilitary crew of Forbidden Planet and expands the United Planets into the United Federation of Planets, the Forbidden Planet Saucer is expanded to a space only starship with projections sticking out of the saucer section.