During the National Bank period, some towns were so small that they managed to have but one National Bank.
Frankston, Kilgore, Lovelady, Rusk, Timpson, and Troupe were such towns.
Some towns had more than one National Bank, but only one at a time. A bank would fail and be replaced by another, but there were never two simultaneously.
Groveton, Trinity, and Kerens were such towns, as were Breckenridge, Burkburnett, and Falfurrias.
They normally retained the same officers, as in Trinity, but the banks' names had to differ. Unlike The Trinity National Bank and The First National Bank of Trinity, the banks' names would often differ in one of two ways. First, the preposition of would be replaced by in, as in Groveton, Breckenridge, Glen Rose, and Electra. Second, the article The would be dropped, as in Kerens. Burkburnett dropped the The and replaced the of at the same time, going directly from The First National Bank of Burkburnett to First National Bank in Burkburnett. At least once, all strategies were used, and The First National Bank of Valley Mills became The First National Bank in Valley Mills, and finally First National Bank in Valley Mills. Not all banks paired by of and in were financially connected. Alvin seems to represent this relationship. At least once, the name of the town changes: The First National Bank of Post City is succeeded by The First National Bank of Post.
Sometimes, the succeeding bank would print notes as its predecessor did, e.g., Groveton and Burkburnett. And sometimes the succeeding bank would not. For example, the second bank in Electra did not issue currency, even though it had a national bank charter number, 13284.

Bank Architecture