I'm not certain what the question is, but Tennessee's multiple party account statute does recognize a tenancy by the entireties in a bank deposit. (Most states do not.) If a bank deposit is owned solely by husband and wife, then it cannot be reached by a garnishment in the name of just one of them. However, it could be reached by a garnishment in both their names.
It's unlikely that there is a statute that spells that out, it's just the way that tenancy by the entireties works and your bank's legal counsel should be able to verify that for you. The difficulty the garnishee bank may face on receipt of a garnishment in the name of only one party to a two party account is in determining whether the account owners are married to each other . Banks normally do not note the parties' marital status and having the same or different last names would not be a reliable indicator.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.