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Chattanooga Municipal is preferable of the two, as it denotes service for other small communities, as well. I personally think "Chattanooga Regional" would be even more correct, as you generate air traffic and passengers from the entire Chattanooga region. The name "Chattanooga Airport" sounds like a small, general aviation airport with few or no corporate landings.
Since you now have aircraft coming in from Europe for Volkswagen, you might try to get an international freight carrier terminal, no matter how small, and then change the name to Chattanooga International Airport. That is what Charlotte/Douglas International Airport did.
Now that is a good idea.