Good job trying this. The one thing I would note is that no one would ever call Franklin a part of West Tennessee. It's always considered Middle Tennessee (and the Grand Divisions have real meaning here). Here would be my TN names:
TN-1: Tri-Cities and Smoky Mountains
TN-2: Knoxville-Maryville
TN-3: Chattanooga-Athens (that's a terrible looking district for not obvious partisan reasons)
TN-4: Murfreesboro-South Cumberland
TN-5: Nashville
TN-6: Lebanon-North Cumberland
TN-7: Williamson-Clarksville
TN-8: Jackson-Germantown
TN-9: Memphis