When the Federalists used that name, they were sending a message that meant those who support a central government. This is because the Federalists believed in a strong central government that could unify the newly formed United States and provide stability and order. They advocated for a Constitution that granted significant powers to the federal government to address issues such as national defense, trade, and taxation. By adopting the name "Federalists," they conveyed their support for a system where the central government had authority over the states in certain matters.
In contrast, the Anti-Federalists, who opposed the Federalists, believed in a more decentralized system where individual states retained more power and autonomy. They were concerned that a strong central government could potentially infringe on states' rights and individual liberties. The debate between Federalists and Anti-Federalists played a crucial role in shaping the structure and principles of the U.S. government as outlined in the Constitution.