1) The name of state may help or may not help: It depends on the product or service you offer. Observe the competitors: Will it give you a competitive advantage (USP) if you mention the name of the state?
2) A state-specific landing page may help to get more detailed statistics in Google Analytics and other Analytic tools. (bounce rate, average visite duration)
If customers thinks that you know the specifics of their state they may trust you more. Simply name droping may not be enough.