Why was federalists an appropriate name for alexander hamilton’s political party?

  Because members believed in a strong federal government

Further detail:

Alexander Hamilton is also known for his key role in writing The Federalist Papers, which were essays he and James Madison and John Jay wrote in favor of the Federalists' position on the need for a strong federal government, advocating ratification of the US Constitution which would give the federal government significantly more powers than the Articles of Confederation had.

The essays that came to be known as The Federalist Papers originally appeared in serial fashion in several newspapers.  85 essays total were then  published in a 2-volume set in 1788, under the title, The Federalist: A Collection of Essays, Written in Favour of the New Constitution, as Agreed upon by the Federal Convention, September 17, 1787.  Of the 85 total essays, Alexander Hamilton wrote 51.