I don’t know if Richard’s reputation is maligned, but I know his brother John got the bad end for reputations.
Richard I (the Lionhearted) was King John's older brother. Richard III came along three centuries later and usurped his nephew Edward V.
Richard the Lionheart may have had a good rep retrospectively, but he deserves a much worse reputation. He held England in contempt, couldn’t even be bothered to learn English, and viewed England simply as a source of power and money to support his wars in France (which he considered his real home) and the crusades in the Holy Land, for which he ravaged England severely in taxes.
His anti-semitic rhetoric also led to a massacre of Jews in London during his coronation.
Richard II wasn’t much better either. During his reign, the peasant’s revolt over poll tax occurred, (although that was an important demonstration to the government that the common people could only be pushed so far) and his brutal intransegence and pettiness led to his deposition and the the brutal slaughter of the Wars of the Roses.