When first digging into this baby name, I was surprised I had never heard it before, since there are several namesakes. The name is traditionally regarded as Polish, although it came from the Old Norse and Icelandic name Rikissa, meaning "wealthy; power." However, other sources suggest it might come from Ricarda, meaning "great ruler." The name has been written as Ryksa, Rixa, Richenza, and Richeza. The name Richenda evolved from Richenza. There are similar, partly related names such as Richmay and Richemaya, Richmal, and Richilda.
Starting with the earliest known namesake, Richeza of Lotharingia, we find that this name is given to royalty more than once. This woman was born about 995 or 1000 to German nobility and married the King of Poland. Although her husband didn't stay king for long, Richeza became a nun and is now known as Blessed Richeza of Lotharingia. She had three children: Casimir I the Restorer, Ryksa, Queen of Hungary, and Gertruda, Grand Princess of Kiev. Her noble descendants went on to rule powerful dynasties, and four of her descendants became saints. They are Irene of Hungary, Princess Margaret of Hungary, Kinga the Duchess of Krakow, and Elisabeth, Landgravine of Thuringia.
Moving on to the next oldest namesake, Richenza of Northeim, who was Duchess of Saxony, Queen of Germany and Holy Roman Empress, it is apparent that this name carries a great deal of historical weight. This noblewoman was born about 1087 and proved to be a great ruler, fighting for the rights of her daughter and grandson.
Richenza of Berg was born about 1095, was Duchess of Bohemia and both of her sisters married nobility.
In 1116 Richeza of Poland was born, the Polish Princess of the House of Piast. She married three times, becoming Princess of Minsk as well. Like Richenza of Lotharingia, this woman also had exceptional ancestors - one of whom was Ingeborg of France. Richeza's grand daughter Richeza of Denmark, born 1180, was the medieval Queen consort of Sweden, married to King Eric X, and her name was in honor of her grandmother. Historical records show that for the six short years Eric was alive in their marriage Richeza only gave birth to girls, and when he died while Richeza was pregnant with their last baby, it turned out to be a boy and the future King of Sweden.
Born 1140 was Ryksa of Castile and Leon, Countess of Provence and Countess Richenza of Everstein, also known as Richeza of Poland. In Castile she was known as Regina Riquilda.
We now come to Richeza of Sweden, wife of Przemysl II of Poland, known as Ryksa Waldemarowna. She most likely had a happy marriage, as her husband demanded he be buried next to her.
Last, there was Elizabeth Richenza of Poland, also known as Eliska Rejcka or Ryksa Elzbieta, yet her name at birth was Richeza. She was the daughter of Richeza of Sweden and Przemysl II, and she became queen consort of Bohemia. When she became Queen of Bohemia she adopted the name Elizabeth because Richeza was seen as a strange name in Bohemia. In her later years she focused on culture, religion and building churches.
In literature I can find only one: Richenda Rayma Anisa of Rheljan, a character in the Deryni series by Katherine Kurtz.