Problem Scenario
You have read about Cato being someone named Reverend William Smith (a fervent loyalist) while George Washington had an affinity for Cato. Who was Cato in the context of the American Revolution?
Answer
There were different Catoes. There needs to be a disambiguation of "Cato."
George Washington's favorite play was Cato by Joseph Addison.
Addison's play is a dramatization of the last days of … Cato (95-46 BCE), who for Addison served as an exemplar of republican virtue and opposition to tyranny.
https://www.mountvernon.org/library/digitalhistory/digital-encyclopedia/article/cato/
Cato was separately a pseudonym of Reverend William Smith who objurgated Common Sense (written by Thomas Paine). To read more about William Smith, a Tory and opponent of the patriotic cause of liberty, and his usage of the alias "Cato", see this Gutenberg.org page. Apparently Thomas Paine wrote what are called "the Forester Letters" to rebut William Smith's "Cato" message (according to www.sethkaller.com).
To read more about the Roman Cato in real life (not just the play), see Brittanica.com.
To read about Cato's Letters written in the early 1700s by men named John Trenchard and Thomas Gordon, you can read a Wikipedia article or an article from the National Constitution Center on them.
Where did the Cato Institute take its name from? The letters that were written by John Trenchard and Thomas Gordon. The source is the first 10 seconds of this video.