Which is why they wrote "The Voyager" in that episode. But it was early in the show, and they hadn't ironed out everything yet. They probably just decided that "the Voyager" sounds awkward (which it does) and so dropped the "the."I assume it's just semantics, something the writers found to be correct but maybe not what Paris would instinctively say. Putting a 'the' in front makes it impersonal maybe? It seems they always say, "back on Voyager" or whatever and never "The Voyager"
And yet, for other ships, they always call it the Enterprise, the Prometheus, the Equinox, etc.