There is no single unified entity known as "First National Bank," but rather hundreds of completely independent financial institutions across the United States that historically incorporated using the phrase "First National Bank" in their title. Because "National" historically denoted a charter granted by the federal Office of the Comptroller of the Currency, dozens of separate, unrelated community and regional banks adopted this descriptor. Consequently, the total number fluctuates constantly as banks merge, rebrand, or get acquired by larger nationwide financial conglomerates.
There is legally no upper limit or maximum restriction on the amount of physical or digital money an individual can deposit and keep in a bank account.