There are often questions posted that ask, "why isn't [fill in the blank] better known today?" Much of the time they're unanswerable, because it's often hard to say why somebody is or is not famous. And, believe me, there are many historical events and historical figures that were and are pretty important that relatively few people know about today. Probably most historians here think their own specialty should be better known.
However, John Rutledge's lack of fame is maybe more explicable. After a pretty heroic time as governor of SC during the War for Independence, Rutledge settled into being a prominent Charleston lawyer and member of the SC General Assembly until 1787. Appointed to be a delegate to the Convention, he was chairman of the Committee of Detail. Unlike some other committees tasked with hard problems ( like, how the new federal government would deal with the states' war debts) his committee had the task of putting into clear legal language all the things were were pretty much agreed upon by the Convention. Because Rutledge was a very good lawyer, he was a good choice, but nothing he and his Committee did was as awe-inspiring as, say, the deal-making of James Madison, or the financial insights of Alexander Hamilton. Apparently he did contribute some useful legal guidance about the function of the Supreme Court, for one thing stipulating that it should only hear cases, not issue advisory opinions on legislation. That's important; but only if you consider what effect an alternative Court, taking an active pre-emptive role in lawmaking, could later have had on the government.
He served briefly on the first Supreme Court for a year, until 1791, and then went back to SC., where he seems to have gone into a decline. He already had had a reputation for being proud and imperious. In 1784 he had a dispute with a Charleston tavernkeeper named Thompson: he had sent a messenger to Thompson asking him to notify the local Irish society, the Sons of St Patrick, that he could not attend their banquet, Thompson claimed he received no such message, that the messenger ( an enslaved Black woman named Beck) only asked if she could watch the Independence Day celebration from an upper window of his tavern. Confronted by Rutledge, Thompson was infuriated when Rutledge believed Beck instead of him. When Thompson expressed himself publicly, Rutledge took advantage of his privileges as a member of the SC Assembly and had him jailed for the rest of the legislative session, about a week,. This at a time when there was already much class tension, with a ruling aristocracy willing to grant clemency to Loyalist landowners wanting to return to SC, but many ( including veterans) wanting them banished. Rutledge was for clemency, Thompson for banishment, so the common population of Charleston was already sensitive about aristocratic privilege and so Thompson's jailing caused a major uproar. After his wife died in 1792, Rutledge seems to have become unstable, likely drinking even more than was usual for a member of the SC elite. Chief Justice John Jay left to become Governor of NY, and then was made an ambassador to England in 1795, to negotiate a very important trade agreement. Rutledge was made Chief Justice by Washington in a recess appointment. When Jay returned, Chief Justice Rutledge startled everyone by speaking out ( and speaking out very harshly, even insultingly) against Jay's treaty. This and probably a general awareness of how much Rutledge's mental health had deteriorated caused the next Congress to refuse to confirm his nomination. He died that year.
So, a simple explanation for his lack of fame is that for the Convention he was competent and useful but not very remarkable, did little that was remarkable after, and died only several years after the Convention.
Stevens, M. E. (1989). Legislative Privilege in Post-Revolutionary South Carolina. The William and Mary Quarterly, 46(1), 71–92. https://doi.org/10.2307/1922408