(1) The use of the word “bank”, “banker”, or “banking”, or words in any foreign language of similar meaning, as a designation or name or part of a designation or name under which business is conducted in this state, is restricted to a national bank, a savings bank subject to this act, a bank, out-of-state bank, a bank holding company, a foreign bank agency, or a foreign bank branch, that is lawfully conducting business in this state, except if the designation or name, taken as a whole, would not imply a banking business.

  (2) A savings bank subject to this act may use the phrase “state savings bank” or “savings bank” as part of a designation or name.