Part of John Muir Trail goes from Tuolumne Meadows to Happy Isles. Many of the trails in the park aren't really named per se, although I know of lot of people informally use names of nearby features to describe them.
There are so many ways you could get from TM to Yosemite Falls. Do you mean trails only, trails, and roads, etc? There's one trail that goes from TM to Tenaya Lake and Olmstead Point.